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The computation power of living systems is maintained by decoherence-free internal quantum states

Abir U. Igamberdiev

Published Jan 1, 2005• 1 citation
OpenAlex

Abstract

The internal quantum state (IQS) is a kind of a pilot-wave (in the Bohmian sense) attached to a macroscopic system and representing its potential field continuously reduced during its exhibition to the external world. This state is maintained as decoherence-free by applying error-correction commands to it and by screening from thermal interactions. Its effective temperature is kept down below the millikelvin range thus being screened even from the background microwave radiation. The quantum Zeno effect enables coherent superpositions and entanglement to persist for macroscopic time intervals. The IQS thus avoids the Boltzmann statistics and approaches a state when the Bose-Einstein statistics is applicable. The IQS of a living system can be viewed as a subtle individual subatomic structure reduced to a complex pattern of vibrating strings and exhibiting itself via a visible classical body-like system. Light quanta inside IQS are trapped like matter is trapped by a black hole in space. The IQS can be considered as a unified field meeting place of gravitational, electromagnetic, weak and strong nuclear forces. The phenomenon of emission of weak coherent light is an indirect evidence of coherent long-living internal quantum states in living systems. This emission is a kind of a similar phenomenon as the Hawking's radiation from black holes and it may serve for unification of the processes taking place in different subsystems of a biological system (synchronization of individual coherent states within the whole system). The external exhibition of the IQS can be expressed as a mapping from complex to real numbers where the certain rules are generated, e.g. the power law and other recursive formulae. In the simplest case when two superposed states are reduced, it has a limit of price of action equal to the Planck's constant. The reduction is non-computable and resembles the act of volition. The result is Godel number appearing above superposed states and memorizing the act of reduction. It is used by living system as an information unit in emerging computation process.

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Living Systems are Dynamically Stable by Computing Themselves at the Quantum Level

Abir U. Igamberdiev

The smallest details of living systems are molecular devices that operate between the classical and quantum levels, i.e. between the potential dimension (microscale) and the actual three-dimensional space (macroscale). They realize non-demolition quantum measurements in which time appears as a mesoscale dimension separating contradictory statements in the course of actualization. These smaller devices form larger devices (macromolecular complexes), up to living body. The quantum device possesses its own potential internal quantum state (IQS), which is maintained for prolonged time via error-correction being a reflection over this state. Decoherence-free IQS can exhibit itself by a creative generation of iteration limits in the real world. To avoid a collapse of the quantum information in the process of correcting errors, it is possible to make a partial measurement that extracts only the error-information and leaves the encoded state untouched. In natural quantum computers, which are living systems, the error-correction is internal. It is a result of reflection, given as a sort of a subjective process allotting optimal limits of iteration. The IQS resembles the properties of a quasi-particle, which interacts with the surround, applying decoherence commands to it. In this framework, enzymes are molecular automata of the extremal quantum computer, the set of which maintains stable highly ordered coherent state, and genome represents a concatenation of error-correcting codes into a single reflective set. Biological systems, being autopoietic in physical space, control quantum measurements in the physical universe. The biological evolution is really a functional evolution of measurement constraints in which limits of iteration are established possessing criteria of perfection and having selective values.

Entropy•Jun 30, 2003•6 citations

Internal Quantum Measurements and the Growth of Information

Abir U. Igamberdiev

Introduction In the processes of adaptation, development and evolution, living systems interpret themselves in the environment resulting in changes of both. This leads to the growth of information via rescaling of internal time (heterochrony) followed by spatial reconstructions of morphology (heterotopy). The growth of information is based on perpetual changes in its interpretation in the changing world. Biological evolution involves the anticipatory epigenetic changes in interpretation of the genetic information which cannot be generally forecasted but can provide canalization of structural changes defined by the existing organization leading to predictable patterns of form generation. Social evolution is accompanied by unprecedented growth of the informational field that leads to progressive development of human society. In modern theoretical biology, the internal measurement concept was suggested as a background for explanation of the phenomenon of life (Matsuno, 1995). The quantum measurement represents the action of a measuring device on the measured system. The quantum measurement is an irreversible phenomenon exhibiting itself as a reduction of the potential field. It has also a relation to the irreversibility of time (Igamberdiev, 1993). The collapse of wave function is not equivalent to time until it does not generate a measurable duration, but when its pattern is repeated consistently, the clock can be set, and the system becomes organized in time. When the measuring device is a part of measured system, the measurement proceeds internally in relation to the whole system and the latter becomes more complex as a result of measurement itself. The aim of this study is to discuss the role of internal measurement in the growth of information in evolving systems. This can refer to biological evolution, social evolution, and as well to the cosmic evolution, which is represented in the phenomenon of expansion of the Universe. Internal Measurement and the Generation of New Information The internal measurement leads to an iterative recursive process which appears as the development and evolution of the combined system containing the measuring device and the measured object. The quantum measuring device can be organized in such way that it “encodes” the system in the course of interaction with the measured object, and makes it possible for the measurement to proceed in a regular way. In this case, such system can memorize the evolutionary complication of organization in a digital information-bearing subsystem and evolve further; in other words it contains an internal description memorizing the result of measurement. The logical precondition of the growth of information in this evolving process is the incompleteness of biosystem’s internal description, while the physical precondition is the uncertainty of quantum measurement. The evolutionary increase of complexity becomes possible when genotype appears as a system distinct from phenotype and is embedded into it, which separates energy-degenerate rate-independent genetic symbols from the rate-dependent dynamics of construction that they control (Pattee, 2001). Evolutionary growth of information becomes its own cause, a universal property of our world. The growth of information accompanies the appearance of measurable time that occurs in the systems performing quantum measurements in a regular way, with low dissipation of energy (Igamberdiev, 1993, 2004). These systems are modelled as hypercycles and can be defined as structures in which the subset of a substrate set of the catalytic system happens to be the matrix for generating and reproducing the set of catalysts itself (Igamberdiev, 1999). This definition keeps the main features of the original notion of hypercycle given by Eigen and Schuster (1979). The hypercyclic system is closed in the way that all of the catalysts needed for an organism to stay alive (representing an efficient causation according to Aristotle and forming organism’s spatiotemporal structure) must be produced by the organism itself, only relying on matter and energy from the outside (Letelier et al., 2011). When hypercycles appear in evolution, time becomes an independent measurable variable due to the internal reproducible changes. Hypercycle organizes irreversibility of quantum measurement into a measurable duration. Eigen’s hypercycle is a formalized representation of the autopoietic system of Maturana and Varela or Rosen’s (M,R) system (Leteiler et al., 2011). The system becomes an internal autonomous clock that distinguishes the past (memory), the present (life), and the future (anticipation based on the reproducible model), so the modeling, logic and digital information growth become possible within the system (Rosen, 1985). The hypercycle having own embedded description, becomes a structure that realizes computation in accordance with its internal logic defined by the embedded description. The latter has the property of incompleteness which is reflected in the fact that quantum correlations of the states of the system are associated with undecidable logic theories, i.e., they can potentially generate the statements not defined within the system. The undecidability can be interpreted in the sense similar to the Gödel’s incompleteness theorem, meaning that there exist propositions, expressible in the formal logic, which cannot be proven or disproven (Briegel et al., 2009). These propositions become the grounds of expansion of the system and its informational growth. From the quantum mechanical point of view, the emergence of a new statement results in acquiring a new error-correction meaning to support the internal quantum state (IQS) (Igamberdiev, 2004, 2007). The IQS keeps the system organizationally invariant. It is supported by the set of error-correcting commands that aim to keep IQS free from external demolitions. The error-correction information becomes an important part of the whole informational field. A new statement makes the system more complex (it leads to an increase of its informational content), with its all spatiotemporal organizational invariance be rescaled. In the course of evolution, an available element of a formal system (similarly to a word when used as a metaphor) can acquire another (in addition to already existing) value that contributes to formation of a new level of organization in the system. The logical basis of this action is the incompleteness of the existing formal system that allows assigning arbitrary values to the statements non-provable within that system, while the physical basis is the quantum uncertainty arising in quantum measurement. A new statement can arise from existing elements by acquiring the double function, however, for fixation of this new statement via expansion of existing formal system, some informational redundancy of the system is needed, which can be achieved by multiplication of some of its elements. Genome is a system which possesses an internal complementarity between the linear texts and their superposition. Relevantly to this, complementarity means that text and hypertext cannot be viewed at the same moment: they should be separated by a time interval. It is an example of uncertainty between the system and its embedding. Overlapping genes, alternatively splicing sequences, RNA and DNA editing, introns, and recombination according to molecular addresses are the features of this hypertext generating a potentially infinite number of language games. Genome as a complete language exists as a complementary set of its alternative combinations resulting in logical paradoxes which determine its temporal dynamics (Isalan, 2009). This superposition is a basis for ontogenesis, adaptation and evolution. Thus, the total “true” genome is a superposition of contradictory arrangements, which generate one single arrangement at a concrete moment of time. The pool of mobile genetic elements expands the combinatorial capacity of the genome by many times. An ambiguity in meaning is analogous to the quantum uncertainty principle in which it is impossible to define strictly the position and impulse of a particle simultaneously, or to fix certain energy in a very short period of time necessary for its registration. The question of a minimal size of the autocatalytic self-reproducing system and its composition has been discussed in several works (Sharov, 2009; Steel et al., 2013). Self-reproduction itself is a creative process of placing text in text with following self-growing of this joint structure. Any evolutionary change also begins from the placing of “text into text”. This is possible because genome is structurally adapted for realization of such a non-trivial function. Moreover, even a point mutation or deletion may be considered as generative if it is placed in the repeated (e.g., diploid) structure. The doubling is a premise of metasystem transition, which includes duplication of the original system and the establishment of control over multiple copies (Turchin, 1977). The evolutionary significance of gene duplication was considered by Ohno (1970) as a premise of neofunctionalization. The advantage of sexual reproduction is in the casual combinatorial generating of new statements from two separate texts that can acquire meanings, thus it resists evolutionary degradation. It becomes a prerequisite for growing of information and complexity (Igamberdiev, 2014). The combinatorial interaction of heterochronic texts generates a new system in which the internal time is rescaled in a new way that generally cannot be forecasted. The heterochronic duplication (via hybridization of temporally different organisms) generates more possibilities for the metasystem transition. Thus, the incompleteness of embedded set of symbols is the formal cause of evolution. The physical representation of this incompleteness is a quantum uncertainty in the course of measurement (Matsuno, 1992). It spans from the level of elementary particles to biological evolution and to the phenomenon of free will and consciousness. Growth of Information in the Expanding Universe The growth of information that we discuss here mainly in relation to biological evolution is relevant also to the physical space-time scales. The self-growing principle of quantum measurement has a property of intrinsic expansion of the informational field. The relationship between observable nature and a hidden “potential” nature is modeled, according to Kineman (2010), as an imaginary space-time domain geometrically represented as radial “Minkowski-space”. Despite of the fact that local space and time are normally represented as real numbers, the general relationship in this geometry is hyperbolic in accordance with the special theory of relativity. When mapped as a radial geometry, the space-time is seen to be intrinsically dynamic (expanding) and self-similar across all scales. The geometry has the properties of early and present acceleration. This representation eliminates the “light cone” and thus all regions in this model are the domains of existence and are observable over time. Nevertheless a domain of general, non-local reality is represented in the imaginary axes that exist simultaneously with measurable, local domains. The Universe in the concept of Kineman (2010) consists of the units called “holons”, which vaguely correspond to Leibniz’s monads. They possess simultaneous properties of location and non-location, as a point of non-differentiated whole appearing in a subject-object relation. The Everett’s interpretation of quantum mechanics works in these isolated domains but not between the domains, the same idea has been suggested by Matsuno (2012) for the individual biological systems taken as separate domains. The reality of superposition of the wave function is limited by the single monad and does not expand outside it, and in this sense monads do not have windows as originally proposed by Leibniz. Conclusion The growth of information is the basic property of evolving systems and it follows from the interaction between non-local and local domains in the course of internal quantum measurements. The internal measurement leads to an iterative recursive process which appears as evolution of the combined system containing the measuring device and the measured object. The system through measurement acquires the property of expansion, which is seen in biological evolution, social development, and at cosmic scales as expansion of the Universe. References Briegel, H.J.; Browne, D.E.; Dur, W.; Raussendorf, R.; Van den Nest, M. Measurement-based quantum computation. Nature Physics 2009, 5, 19-26. Eigen, M.; Schuster, P. The Hypercycle: A Principle of Natural Self-Organization. Springer, Berlin, 1979. Igamberdiev, A.U. Quantum mechanical properties of biosystems: A framework for complexity, structural stability and transformations. Biosystems 1993, 31, 65‐ Igamberdiev, A.U. Foundations of metabolic organization: coherence as a basis of computational properties in metabolic networks. Biosystems 1999, 50, 1-16. Igamberdiev, A.U. Quantum computation, non-demolition measurements, and reflective control in living systems. Biosystems 2004, 77, 47–56. Igamberdiev, A.U. Physical limits of computation and emergence of life. Biosystems 2007, 90, 340–349. Igamberdiev, A.U. Time rescaling and pattern formation in biological evolution. Biosystems 2014, 123, 19-26. Isalan, M. Gene networks and liar paradoxes. Bioessays 2009, 31, 1110-1115. Letelier, J.C.; Cárdenas, M.L.; Cornish-Bowden, A. From L'Homme Machine to metabolic closure: steps towards understanding life. Journal of Theoretical Biology 2011, 286, 100-113. Matsuno, K. The uncertainty principle as an evolutionary engine. Biosystems 1991, 27, 63-76. Matsuno, K. Quantum and biological computation. Biosystems 1995, 35, 209-212. Matsuno, K. Chemical evolution as a concrete scheme for naturalizing the relative-state of quantum mechanics. Biosystems 2012, 109, 159-168. Kineman, J.J. Relational self-similar space-time cosmology revisited. Proceedings of the 54th Meeting of the International Society for System Sciences. Waterloo, Canada, 2010. Ohno, S. Evolution by Gene Duplication. Springer, New York, 1970. Pattee, H.H. The physics of symbols: bridging the epistemic cut. Biosystems 2001, 60, 5-21. Sharov, A.A., 2009. Coenzyme autocatalytic network on the surface of oil microspheres as a model for the origin of life. International Journal of Molecular Sciences 2009, 10, 1838-1852. Steel, M.; Hordijk, W.; Smith, J. Minimal autocatalytic networks. Journal of Theoretical Biology 2013, 332, 96-107. Turchin, V. Phenomenon of Science. Columbia University Press, New York, 1977.

ISIS Summit: The Information Society at the Crossroads•Jun 23, 2015•0 citations

A REPORT ON QUANTUM COMPUTING

Achintya A. Paradkar

Today's computers work on bits that exist as either 0 or 1. Quantum computers aren't limited to two states; they encode information as quantum bits, or qubits, which can exist in superposition. Qubits represent atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and a processor. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today's most powerful supercomputers. A processor that can use registers of qubits will be able to perform calculations using all the possible values of the input registers simultaneously. This superposition causes a phenomenon called quantum parallelism, and is the motivating force behind the research being carried out in quantum computing. Due to technical obstacles, till date, a quantum computer has not yet been realized. But the concepts and ideas of quantum computing has been demonstrated using various methods like NMR, Ion Trap, Quantum Dot, Optical Methods, etc. A quantum computer manipulates qubits by executing a series of quantum gates, each a unitary transformation acting on a single qubit or pair of qubits. In applying these gates in succession, a quantum computer can perform a complicated unitary transformation to a set of qubits in some initial state. The qubits can then be measured, with this measurement serving as the final computational result. Research must devise a way to maintain decoherence and other potential sources of error at an acceptable level. Probably the most important idea in this field is the application of error correction in phase coherence as a means to extract information and reduce error in a quantum system without actually measuring that system. Thereby, quantum computers will emerge as the superior computational devices and perhaps one day make today's modern computer obsolete.

International Journal of Students Research in Technology & Management•Sep 26, 2015•1 citation

How to control decoherence and entanglement in quantum complex systems?

V. M. Akulin, Gershon Kurizki, Daniel A. Lidar

Theory and experiment have not fully resolved the apparent dichotomy , which has agonized physics for the past eighty years: on the one hand, the description of microsystems by quantum mechanics and, on the other, the description of macrosystems by classical dynamics or statistical mechanics. Derivations of the time-irreversible Liouville equation for an open quantum system, based on projecting out its environment, have narrowed the gap between the quantum and classical descriptions. Yet our `classical' intuition continues to be confronted by quantum-mechanical results like the Einstein--Podolsky--Rosen paradox that challenges the classical notion of locality, or the quantum Zeno effect which suggests that the isolation of a system is not the only way to preserve its quantum state. There are two key concepts in any discussion of such issues. The first, which is responsible for the most salient nonclassical properties, is entanglement , that is partial or complete correlation or, more generally, inseparability of the elements comprising a quantum ensemble . Even after their interaction has ceased, this inseparability, originating from their past interaction, can affect the state of one element when another element is subject to a nonunitary action, such as its measurement, tracing- out, or thermalization. The second key concept is decoherence of open quantum systems, which is the consequence of their entanglement with their environment, a `meter' or a thermal `reservoir', followed by the tracing-out of the latter. Despite new insights into entanglement and decoherence, there are still no complete, unequivocal answers to the fundamental questions of the transition from quantal to classical behaviour: how do irreversibility and classicality emerge from unitarity as systems and their environments become increasingly complex ? 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In order to resolve the outstanding issues of the quantum--classical transition, and study the control of entanglement and decoherence without the foregoing restrictions, we must venture into the domain of Quantum Complex Systems (QUACS), either consisting of a large number of inseparable elements or having many coupled degrees of freedom. Our conviction is that fundamental understanding and manipulation of entanglement within QUACS or their entanglement with the environment or a meter, call for the creation of a new conceptual framework or paradigm, that would encompass phenomena common to cold atoms in laser fields, large molecules, Josephson junctions, quantum gases and solids, with the view of employing these systems for quantum information processing and computing. Progress within this paradigm should allow us to answer the questions: does entanglement play an essential role in the evolution of large collections of complex systems? What are the size and complexity limits of systems and ensembles still controllable by an external intervention? What are the most appropriate decoherence protection schemes and control algorithms? This special issue addresses the challenge of understanding in depth and manipulating the basic quantum properties of optical, atomic, molecular and condensed-matter QUACS, and large ensembles thereof. In view of the interdisciplinary character of this issue, we find it expedient to look at the presented articles not only according to the physical objects they describe, but also from a unifying standpoint. Several unifying themes may be discerned: memory effects in dephasing and relaxation; protection of quantum information by its distribution throughout the ensemble; control of decoherence and entanglement by time-dependent interventions or measurements; manifestations of entanglement in scattering off statistical ensembles; measurment-induced dynamics. The concerted discussion of the topics outlined above should help us advance the new paradigm that addresses our abilities to diagnose and manipulate the entangled states of complex quantum objects and their robustness against decoherence. These abilities are required for quantum information (QI) applications in matter--wave interferometry in molecular, semiconducting or superconducting systems. On the fundamental level, this book may help establish the notion of dynamical information exchange between quantum systems and chart in detail the route from unitarity to classicality. Further developments within the outlined paradigm should yield novel, advantageous QI processing schemes and high-sensitivity interferometers, owing to decoherence suppression and effective control of many degrees of freedom. In the long run, these strategies may prove to be the first step towards the (hitherto unattempted) use of entanglement in nanotechnology, metrology and chemistry, with potentially remarkable novel applications.

Journal of Physics B Atomic Molecular and Optical Physics•Apr 18, 2007•2 citations

The emergence of complex biological organization at the interface of quantum and gravity

N.Ž. Mišić

The existence of living organisms in the mesoscopic realm may be quite nontrivial and actuallymay emerge from the interplay between quantum mechanics and gravity. On one side, quantumbiology investigates how quantum mechanical phenomena, such as superposition, entanglement,and tunnelling, contribute to biological processes. These quantum effects, once thought to beirrelevant in the “warm, wet, and noisy” environment of living organisms due to decoherence, havebeen found to play significant roles in various biological systems, from photosynthesis to enzymecatalysis. On the other side, gravitational forces have been implicated in the organization ofmicrotubules, which are essential for maintaining cellular structure and function. Recent studieshave demonstrated that gravitational forces can induce three-dimensional chromosomal conformational changes, which are associated with rapid transcriptional responses in human T cells. Sometheories propose that gravity might play a role in decoherence, such as in the Penrose-Hameroffmodel, which proposes that quantum coherence in microtubules could be the basis for consciousawareness and quantum computing-like information processing, with gravity playing a role in thecollapse of the quantum wave function. The model predictions that microtubules can support longrange coherent phenomena have been confirmed by experimental observations of superradiancefrom mega-networks of tryptophan UV-excited transition dipoles, particularly in microtubulearchitectures. Another experimental research highlights that microtubule network exhibits ahierarchy of three-fold resonant frequency patterns across biological scales – from tubulin proteinsto microtubules and neurons. This suggests a quantum-to-classical transition governed by scalefree dynamics, potentially underlying information processing in the brain. A very intriguing fact isthat at the most fundamental level of the origin of life, the standard genetic code, we can observethe scale-free computing that arises from arithmetic regularities of the nucleon numbers related tothe code’s numerous symmetries. Given that some of these symmetries probably originate fromdifferent evolutionary epochs, such scale-free computing may be a latent background mechanismof the organization of the genetic code and therefore relevant to natural computing.

•Apr 29, 2025•0 citations

Decoherence and the Appearance of a Classical World in Quantum Theory

Robert Alicki

In the last decade decoherence has become a very popular topic mainly due to the progress in experimental techniques which allow monitoring of the process of decoherence for single microscopic or mesoscopic systems. The other motivation is the rapid development of quantum information and quantum computation theory where decoherence is the main obstacle in the implementation of bold theoretical ideas. All that makes the second improved and extended edition of this book very timely. Despite the enormous efforts of many authors decoherence with its consequences still remains a rather controversial subject. It touches on, namely, the notoriously confusing issues of quantum measurement theory and interpretation of quantum mechanics. The existence of different points of view is reflected by the structure and content of the book. The first three authors (Joos, Zeh and Kiefer) accept the standard formalism of quantum mechanics but seem to reject orthodox Copenhagen interpretation, Giulini and Kupsch stick to both while Stamatescu discusses models which go beyond the standard quantum theory. Fortunately, most of the presented results are independent of the interpretation and the mathematical formalism is common for the (meta)physically different approaches. After a short introduction by Joos followed by a more detailed review of the basic concepts by Zeh, chapter 3 (the longest chapter) by Joos is devoted to the environmental decoherence. Here the author considers mostly rather `down to earth' and well-motivated mechanisms of decoherence through collisions with atoms or molecules and the processes of emission, absorption and scattering of photons. The issues of decoherence induced superselection rules and localization of objects including the possible explanation of the molecular structure are discussed in details. Many other topics are also reviewed in this chapter, e.g., the so-called Zeno effect, relationships between quantum chaos and decoherence, the role of decoherence in quantum information processing and even decoherence in the brain. The next chapter, written by Kiefer, is devoted to decoherence in quantum field theory and quantum gravity which is a much more speculative and less explored topic. Two complementary aspects are studied in this approach: decoherence of particle states by the quantum fields and decoherence of field states by the particles. Cosmological issues related to decoherence are discussed, not only within the standard Friedmann cosmology, but also using the elements of the theory of black holes, wormholes and strings. The relations between the formalism of consistent histories defined in terms of decoherence functionals and the environmental decoherence are discussed in chapter 5, also written by Kiefer. The Feynman--Vernon influence functional for the quantum open system is presented in detail as the first example of decoherence functional. Then the general theory is outlined together with possible interpretations including cosmological aspects. The next chapter by Giulini presents an overview of the superselection rules arising from physical symmetries and gauge transformations both for nonrelativistic quantum mechanics and quantum field theory. Critical discussion of kinematical superselection rules versus dynamical ones is illustrated by numerous examples like Galilei invariant quantum mechanics, quantum electrodynamics and quantum gravity. The introduction to the theory of quantum open systems and its applications to decoherence models is given in chapter 7 by Kupsch. Generalized master equations, Markovian approximation and a few Hamiltonian models relevant for decoherence are discussed. Some mathematical tools, e.g., complete positivity and entropy inequalities are also presented. The last chapter by Stamatescu is devoted to stochastic collapse models which can be interpreted either as certain representations of the dynamics of open quantum systems or as fundamental modifications of the Schr\"odinger equation. The final part of the book consists of remarks by Zeh on related concepts and methods and seven appendices. The broad spectrum, mathematically-friendly presentation, inclusion of the very recent developments and the extensive bibliography (about 550 references) make this book a valuable reference for all researchers, graduate and PhD students interested in the foundations of quantum mechanics, quantum open systems and quantum information. The relative independence of the chapters and numerous redundancies allow for selective reading, which is very helpful for newcomers to this field.

Journal of Physics A Mathematical and General•Jan 19, 2004•64 citations
The internal quantum state (IQS) is a kind of a pilot-wave (in the Bohmian sense) attached to a macroscopic system and representing its potential field continuously reduced during its exhibition to the external world. This state is maintained as decoherence-free by applying error-correction commands to it and by screening from thermal interactions. Its effective temperature is kept down below the millikelvin range thus being screened even from the background microwave radiation. The quantum Zeno effect enables coherent superpositions and entanglement to persist for macroscopic time intervals. The IQS thus avoids the Boltzmann statistics and approaches a state when the Bose-Einstein statistics is applicable. The IQS of a living system can be viewed as a subtle individual subatomic structure reduced to a complex pattern of vibrating strings and exhibiting itself via a visible classical body-like system. Light quanta inside IQS are trapped like matter is trapped by a black hole in space. The IQS can be considered as a unified field meeting place of gravitational, electromagnetic, weak and strong nuclear forces. The phenomenon of emission of weak coherent light is an indirect evidence of coherent long-living internal quantum states in living systems. This emission is a kind of a similar phenomenon as the Hawking's radiation from black holes and it may serve for unification of the processes taking place in different subsystems of a biological system (synchronization of individual coherent states within the whole system). The external exhibition of the IQS can be expressed as a mapping from complex to real numbers where the certain rules are generated, e.g. the power law and other recursive formulae. In the simplest case when two superposed states are reduced, it has a limit of price of action equal to the Planck's constant. The reduction is non-computable and resembles the act of volition. The result is Godel number appearing above superposed states and memorizing the act of reduction. It is used by living system as an information unit in emerging computation process.
The smallest details of living systems are molecular devices that operate between the classical and quantum levels, i.e. between the potential dimension (microscale) and the actual three-dimensional space (macroscale). They realize non-demolition quantum measurements in which time appears as a mesoscale dimension separating contradictory statements in the course of actualization. These smaller devices form larger devices (macromolecular complexes), up to living body. The quantum device possesses its own potential internal quantum state (IQS), which is maintained for prolonged time via error-correction being a reflection over this state. Decoherence-free IQS can exhibit itself by a creative generation of iteration limits in the real world. To avoid a collapse of the quantum information in the process of correcting errors, it is possible to make a partial measurement that extracts only the error-information and leaves the encoded state untouched. In natural quantum computers, which are living systems, the error-correction is internal. It is a result of reflection, given as a sort of a subjective process allotting optimal limits of iteration. The IQS resembles the properties of a quasi-particle, which interacts with the surround, applying decoherence commands to it. In this framework, enzymes are molecular automata of the extremal quantum computer, the set of which maintains stable highly ordered coherent state, and genome represents a concatenation of error-correcting codes into a single reflective set. Biological systems, being autopoietic in physical space, control quantum measurements in the physical universe. The biological evolution is really a functional evolution of measurement constraints in which limits of iteration are established possessing criteria of perfection and having selective values.
Introduction In the processes of adaptation, development and evolution, living systems interpret themselves in the environment resulting in changes of both. This leads to the growth of information via rescaling of internal time (heterochrony) followed by spatial reconstructions of morphology (heterotopy). The growth of information is based on perpetual changes in its interpretation in the changing world. Biological evolution involves the anticipatory epigenetic changes in interpretation of the genetic information which cannot be generally forecasted but can provide canalization of structural changes defined by the existing organization leading to predictable patterns of form generation. Social evolution is accompanied by unprecedented growth of the informational field that leads to progressive development of human society. In modern theoretical biology, the internal measurement concept was suggested as a background for explanation of the phenomenon of life (Matsuno, 1995). The quantum measurement represents the action of a measuring device on the measured system. The quantum measurement is an irreversible phenomenon exhibiting itself as a reduction of the potential field. It has also a relation to the irreversibility of time (Igamberdiev, 1993). The collapse of wave function is not equivalent to time until it does not generate a measurable duration, but when its pattern is repeated consistently, the clock can be set, and the system becomes organized in time. When the measuring device is a part of measured system, the measurement proceeds internally in relation to the whole system and the latter becomes more complex as a result of measurement itself. The aim of this study is to discuss the role of internal measurement in the growth of information in evolving systems. This can refer to biological evolution, social evolution, and as well to the cosmic evolution, which is represented in the phenomenon of expansion of the Universe. Internal Measurement and the Generation of New Information The internal measurement leads to an iterative recursive process which appears as the development and evolution of the combined system containing the measuring device and the measured object. The quantum measuring device can be organized in such way that it “encodes” the system in the course of interaction with the measured object, and makes it possible for the measurement to proceed in a regular way. In this case, such system can memorize the evolutionary complication of organization in a digital information-bearing subsystem and evolve further; in other words it contains an internal description memorizing the result of measurement. The logical precondition of the growth of information in this evolving process is the incompleteness of biosystem’s internal description, while the physical precondition is the uncertainty of quantum measurement. The evolutionary increase of complexity becomes possible when genotype appears as a system distinct from phenotype and is embedded into it, which separates energy-degenerate rate-independent genetic symbols from the rate-dependent dynamics of construction that they control (Pattee, 2001). Evolutionary growth of information becomes its own cause, a universal property of our world. The growth of information accompanies the appearance of measurable time that occurs in the systems performing quantum measurements in a regular way, with low dissipation of energy (Igamberdiev, 1993, 2004). These systems are modelled as hypercycles and can be defined as structures in which the subset of a substrate set of the catalytic system happens to be the matrix for generating and reproducing the set of catalysts itself (Igamberdiev, 1999). This definition keeps the main features of the original notion of hypercycle given by Eigen and Schuster (1979). The hypercyclic system is closed in the way that all of the catalysts needed for an organism to stay alive (representing an efficient causation according to Aristotle and forming organism’s spatiotemporal structure) must be produced by the organism itself, only relying on matter and energy from the outside (Letelier et al., 2011). When hypercycles appear in evolution, time becomes an independent measurable variable due to the internal reproducible changes. Hypercycle organizes irreversibility of quantum measurement into a measurable duration. Eigen’s hypercycle is a formalized representation of the autopoietic system of Maturana and Varela or Rosen’s (M,R) system (Leteiler et al., 2011). The system becomes an internal autonomous clock that distinguishes the past (memory), the present (life), and the future (anticipation based on the reproducible model), so the modeling, logic and digital information growth become possible within the system (Rosen, 1985). The hypercycle having own embedded description, becomes a structure that realizes computation in accordance with its internal logic defined by the embedded description. The latter has the property of incompleteness which is reflected in the fact that quantum correlations of the states of the system are associated with undecidable logic theories, i.e., they can potentially generate the statements not defined within the system. The undecidability can be interpreted in the sense similar to the Gödel’s incompleteness theorem, meaning that there exist propositions, expressible in the formal logic, which cannot be proven or disproven (Briegel et al., 2009). These propositions become the grounds of expansion of the system and its informational growth. From the quantum mechanical point of view, the emergence of a new statement results in acquiring a new error-correction meaning to support the internal quantum state (IQS) (Igamberdiev, 2004, 2007). The IQS keeps the system organizationally invariant. It is supported by the set of error-correcting commands that aim to keep IQS free from external demolitions. The error-correction information becomes an important part of the whole informational field. A new statement makes the system more complex (it leads to an increase of its informational content), with its all spatiotemporal organizational invariance be rescaled. In the course of evolution, an available element of a formal system (similarly to a word when used as a metaphor) can acquire another (in addition to already existing) value that contributes to formation of a new level of organization in the system. The logical basis of this action is the incompleteness of the existing formal system that allows assigning arbitrary values to the statements non-provable within that system, while the physical basis is the quantum uncertainty arising in quantum measurement. A new statement can arise from existing elements by acquiring the double function, however, for fixation of this new statement via expansion of existing formal system, some informational redundancy of the system is needed, which can be achieved by multiplication of some of its elements. Genome is a system which possesses an internal complementarity between the linear texts and their superposition. Relevantly to this, complementarity means that text and hypertext cannot be viewed at the same moment: they should be separated by a time interval. It is an example of uncertainty between the system and its embedding. Overlapping genes, alternatively splicing sequences, RNA and DNA editing, introns, and recombination according to molecular addresses are the features of this hypertext generating a potentially infinite number of language games. Genome as a complete language exists as a complementary set of its alternative combinations resulting in logical paradoxes which determine its temporal dynamics (Isalan, 2009). This superposition is a basis for ontogenesis, adaptation and evolution. Thus, the total “true” genome is a superposition of contradictory arrangements, which generate one single arrangement at a concrete moment of time. The pool of mobile genetic elements expands the combinatorial capacity of the genome by many times. An ambiguity in meaning is analogous to the quantum uncertainty principle in which it is impossible to define strictly the position and impulse of a particle simultaneously, or to fix certain energy in a very short period of time necessary for its registration. The question of a minimal size of the autocatalytic self-reproducing system and its composition has been discussed in several works (Sharov, 2009; Steel et al., 2013). Self-reproduction itself is a creative process of placing text in text with following self-growing of this joint structure. Any evolutionary change also begins from the placing of “text into text”. This is possible because genome is structurally adapted for realization of such a non-trivial function. Moreover, even a point mutation or deletion may be considered as generative if it is placed in the repeated (e.g., diploid) structure. The doubling is a premise of metasystem transition, which includes duplication of the original system and the establishment of control over multiple copies (Turchin, 1977). The evolutionary significance of gene duplication was considered by Ohno (1970) as a premise of neofunctionalization. The advantage of sexual reproduction is in the casual combinatorial generating of new statements from two separate texts that can acquire meanings, thus it resists evolutionary degradation. It becomes a prerequisite for growing of information and complexity (Igamberdiev, 2014). The combinatorial interaction of heterochronic texts generates a new system in which the internal time is rescaled in a new way that generally cannot be forecasted. The heterochronic duplication (via hybridization of temporally different organisms) generates more possibilities for the metasystem transition. Thus, the incompleteness of embedded set of symbols is the formal cause of evolution. The physical representation of this incompleteness is a quantum uncertainty in the course of measurement (Matsuno, 1992). It spans from the level of elementary particles to biological evolution and to the phenomenon of free will and consciousness. Growth of Information in the Expanding Universe The growth of information that we discuss here mainly in relation to biological evolution is relevant also to the physical space-time scales. The self-growing principle of quantum measurement has a property of intrinsic expansion of the informational field. The relationship between observable nature and a hidden “potential” nature is modeled, according to Kineman (2010), as an imaginary space-time domain geometrically represented as radial “Minkowski-space”. Despite of the fact that local space and time are normally represented as real numbers, the general relationship in this geometry is hyperbolic in accordance with the special theory of relativity. When mapped as a radial geometry, the space-time is seen to be intrinsically dynamic (expanding) and self-similar across all scales. The geometry has the properties of early and present acceleration. This representation eliminates the “light cone” and thus all regions in this model are the domains of existence and are observable over time. Nevertheless a domain of general, non-local reality is represented in the imaginary axes that exist simultaneously with measurable, local domains. The Universe in the concept of Kineman (2010) consists of the units called “holons”, which vaguely correspond to Leibniz’s monads. They possess simultaneous properties of location and non-location, as a point of non-differentiated whole appearing in a subject-object relation. The Everett’s interpretation of quantum mechanics works in these isolated domains but not between the domains, the same idea has been suggested by Matsuno (2012) for the individual biological systems taken as separate domains. The reality of superposition of the wave function is limited by the single monad and does not expand outside it, and in this sense monads do not have windows as originally proposed by Leibniz. Conclusion The growth of information is the basic property of evolving systems and it follows from the interaction between non-local and local domains in the course of internal quantum measurements. The internal measurement leads to an iterative recursive process which appears as evolution of the combined system containing the measuring device and the measured object. The system through measurement acquires the property of expansion, which is seen in biological evolution, social development, and at cosmic scales as expansion of the Universe. References Briegel, H.J.; Browne, D.E.; Dur, W.; Raussendorf, R.; Van den Nest, M. Measurement-based quantum computation. Nature Physics 2009, 5, 19-26. Eigen, M.; Schuster, P. The Hypercycle: A Principle of Natural Self-Organization. Springer, Berlin, 1979. Igamberdiev, A.U. Quantum mechanical properties of biosystems: A framework for complexity, structural stability and transformations. Biosystems 1993, 31, 65‐ Igamberdiev, A.U. Foundations of metabolic organization: coherence as a basis of computational properties in metabolic networks. Biosystems 1999, 50, 1-16. Igamberdiev, A.U. Quantum computation, non-demolition measurements, and reflective control in living systems. Biosystems 2004, 77, 47–56. Igamberdiev, A.U. Physical limits of computation and emergence of life. Biosystems 2007, 90, 340–349. Igamberdiev, A.U. Time rescaling and pattern formation in biological evolution. Biosystems 2014, 123, 19-26. Isalan, M. Gene networks and liar paradoxes. Bioessays 2009, 31, 1110-1115. Letelier, J.C.; Cárdenas, M.L.; Cornish-Bowden, A. From L'Homme Machine to metabolic closure: steps towards understanding life. Journal of Theoretical Biology 2011, 286, 100-113. Matsuno, K. The uncertainty principle as an evolutionary engine. Biosystems 1991, 27, 63-76. Matsuno, K. Quantum and biological computation. Biosystems 1995, 35, 209-212. Matsuno, K. Chemical evolution as a concrete scheme for naturalizing the relative-state of quantum mechanics. Biosystems 2012, 109, 159-168. Kineman, J.J. Relational self-similar space-time cosmology revisited. Proceedings of the 54th Meeting of the International Society for System Sciences. Waterloo, Canada, 2010. Ohno, S. Evolution by Gene Duplication. Springer, New York, 1970. Pattee, H.H. The physics of symbols: bridging the epistemic cut. Biosystems 2001, 60, 5-21. Sharov, A.A., 2009. Coenzyme autocatalytic network on the surface of oil microspheres as a model for the origin of life. International Journal of Molecular Sciences 2009, 10, 1838-1852. Steel, M.; Hordijk, W.; Smith, J. Minimal autocatalytic networks. Journal of Theoretical Biology 2013, 332, 96-107. Turchin, V. Phenomenon of Science. Columbia University Press, New York, 1977.
Today's computers work on bits that exist as either 0 or 1. Quantum computers aren't limited to two states; they encode information as quantum bits, or qubits, which can exist in superposition. Qubits represent atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and a processor. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today's most powerful supercomputers. A processor that can use registers of qubits will be able to perform calculations using all the possible values of the input registers simultaneously. This superposition causes a phenomenon called quantum parallelism, and is the motivating force behind the research being carried out in quantum computing. Due to technical obstacles, till date, a quantum computer has not yet been realized. But the concepts and ideas of quantum computing has been demonstrated using various methods like NMR, Ion Trap, Quantum Dot, Optical Methods, etc. A quantum computer manipulates qubits by executing a series of quantum gates, each a unitary transformation acting on a single qubit or pair of qubits. In applying these gates in succession, a quantum computer can perform a complicated unitary transformation to a set of qubits in some initial state. The qubits can then be measured, with this measurement serving as the final computational result. Research must devise a way to maintain decoherence and other potential sources of error at an acceptable level. Probably the most important idea in this field is the application of error correction in phase coherence as a means to extract information and reduce error in a quantum system without actually measuring that system. Thereby, quantum computers will emerge as the superior computational devices and perhaps one day make today's modern computer obsolete.
Theory and experiment have not fully resolved the apparent dichotomy , which has agonized physics for the past eighty years: on the one hand, the description of microsystems by quantum mechanics and, on the other, the description of macrosystems by classical dynamics or statistical mechanics. Derivations of the time-irreversible Liouville equation for an open quantum system, based on projecting out its environment, have narrowed the gap between the quantum and classical descriptions. Yet our `classical' intuition continues to be confronted by quantum-mechanical results like the Einstein--Podolsky--Rosen paradox that challenges the classical notion of locality, or the quantum Zeno effect which suggests that the isolation of a system is not the only way to preserve its quantum state. There are two key concepts in any discussion of such issues. The first, which is responsible for the most salient nonclassical properties, is entanglement , that is partial or complete correlation or, more generally, inseparability of the elements comprising a quantum ensemble . Even after their interaction has ceased, this inseparability, originating from their past interaction, can affect the state of one element when another element is subject to a nonunitary action, such as its measurement, tracing- out, or thermalization. The second key concept is decoherence of open quantum systems, which is the consequence of their entanglement with their environment, a `meter' or a thermal `reservoir', followed by the tracing-out of the latter. Despite new insights into entanglement and decoherence, there are still no complete, unequivocal answers to the fundamental questions of the transition from quantal to classical behaviour: how do irreversibility and classicality emerge from unitarity as systems and their environments become increasingly complex ? At what stage does system--meter entanglement give rise to a classical readout of the meter? Is there an upper limit on the size or complexity of systems displaying entanglement? Major developments have opened new vistas into controlled entanglement , which is the resource of quantum information processing. However, these developments have mainly focused on ensembles of simple two- and three-level systems that are thoroughly isolated from their environments. Treatments of coherence in quantum computing have mostly assumed that only a single or a few the elements of the quantum ensemble may simultaneously undergo an uncontrolled intervention---a quantum error. Decoherence-control protocols for more general types of errors are still incomplete. In order to resolve the outstanding issues of the quantum--classical transition, and study the control of entanglement and decoherence without the foregoing restrictions, we must venture into the domain of Quantum Complex Systems (QUACS), either consisting of a large number of inseparable elements or having many coupled degrees of freedom. Our conviction is that fundamental understanding and manipulation of entanglement within QUACS or their entanglement with the environment or a meter, call for the creation of a new conceptual framework or paradigm, that would encompass phenomena common to cold atoms in laser fields, large molecules, Josephson junctions, quantum gases and solids, with the view of employing these systems for quantum information processing and computing. Progress within this paradigm should allow us to answer the questions: does entanglement play an essential role in the evolution of large collections of complex systems? What are the size and complexity limits of systems and ensembles still controllable by an external intervention? What are the most appropriate decoherence protection schemes and control algorithms? This special issue addresses the challenge of understanding in depth and manipulating the basic quantum properties of optical, atomic, molecular and condensed-matter QUACS, and large ensembles thereof. In view of the interdisciplinary character of this issue, we find it expedient to look at the presented articles not only according to the physical objects they describe, but also from a unifying standpoint. Several unifying themes may be discerned: memory effects in dephasing and relaxation; protection of quantum information by its distribution throughout the ensemble; control of decoherence and entanglement by time-dependent interventions or measurements; manifestations of entanglement in scattering off statistical ensembles; measurment-induced dynamics. The concerted discussion of the topics outlined above should help us advance the new paradigm that addresses our abilities to diagnose and manipulate the entangled states of complex quantum objects and their robustness against decoherence. These abilities are required for quantum information (QI) applications in matter--wave interferometry in molecular, semiconducting or superconducting systems. On the fundamental level, this book may help establish the notion of dynamical information exchange between quantum systems and chart in detail the route from unitarity to classicality. Further developments within the outlined paradigm should yield novel, advantageous QI processing schemes and high-sensitivity interferometers, owing to decoherence suppression and effective control of many degrees of freedom. In the long run, these strategies may prove to be the first step towards the (hitherto unattempted) use of entanglement in nanotechnology, metrology and chemistry, with potentially remarkable novel applications.
The existence of living organisms in the mesoscopic realm may be quite nontrivial and actuallymay emerge from the interplay between quantum mechanics and gravity. On one side, quantumbiology investigates how quantum mechanical phenomena, such as superposition, entanglement,and tunnelling, contribute to biological processes. These quantum effects, once thought to beirrelevant in the “warm, wet, and noisy” environment of living organisms due to decoherence, havebeen found to play significant roles in various biological systems, from photosynthesis to enzymecatalysis. On the other side, gravitational forces have been implicated in the organization ofmicrotubules, which are essential for maintaining cellular structure and function. Recent studieshave demonstrated that gravitational forces can induce three-dimensional chromosomal conformational changes, which are associated with rapid transcriptional responses in human T cells. Sometheories propose that gravity might play a role in decoherence, such as in the Penrose-Hameroffmodel, which proposes that quantum coherence in microtubules could be the basis for consciousawareness and quantum computing-like information processing, with gravity playing a role in thecollapse of the quantum wave function. The model predictions that microtubules can support longrange coherent phenomena have been confirmed by experimental observations of superradiancefrom mega-networks of tryptophan UV-excited transition dipoles, particularly in microtubulearchitectures. Another experimental research highlights that microtubule network exhibits ahierarchy of three-fold resonant frequency patterns across biological scales – from tubulin proteinsto microtubules and neurons. This suggests a quantum-to-classical transition governed by scalefree dynamics, potentially underlying information processing in the brain. A very intriguing fact isthat at the most fundamental level of the origin of life, the standard genetic code, we can observethe scale-free computing that arises from arithmetic regularities of the nucleon numbers related tothe code’s numerous symmetries. Given that some of these symmetries probably originate fromdifferent evolutionary epochs, such scale-free computing may be a latent background mechanismof the organization of the genetic code and therefore relevant to natural computing.
In the last decade decoherence has become a very popular topic mainly due to the progress in experimental techniques which allow monitoring of the process of decoherence for single microscopic or mesoscopic systems. The other motivation is the rapid development of quantum information and quantum computation theory where decoherence is the main obstacle in the implementation of bold theoretical ideas. All that makes the second improved and extended edition of this book very timely. Despite the enormous efforts of many authors decoherence with its consequences still remains a rather controversial subject. It touches on, namely, the notoriously confusing issues of quantum measurement theory and interpretation of quantum mechanics. The existence of different points of view is reflected by the structure and content of the book. The first three authors (Joos, Zeh and Kiefer) accept the standard formalism of quantum mechanics but seem to reject orthodox Copenhagen interpretation, Giulini and Kupsch stick to both while Stamatescu discusses models which go beyond the standard quantum theory. Fortunately, most of the presented results are independent of the interpretation and the mathematical formalism is common for the (meta)physically different approaches. After a short introduction by Joos followed by a more detailed review of the basic concepts by Zeh, chapter 3 (the longest chapter) by Joos is devoted to the environmental decoherence. Here the author considers mostly rather `down to earth' and well-motivated mechanisms of decoherence through collisions with atoms or molecules and the processes of emission, absorption and scattering of photons. The issues of decoherence induced superselection rules and localization of objects including the possible explanation of the molecular structure are discussed in details. Many other topics are also reviewed in this chapter, e.g., the so-called Zeno effect, relationships between quantum chaos and decoherence, the role of decoherence in quantum information processing and even decoherence in the brain. The next chapter, written by Kiefer, is devoted to decoherence in quantum field theory and quantum gravity which is a much more speculative and less explored topic. Two complementary aspects are studied in this approach: decoherence of particle states by the quantum fields and decoherence of field states by the particles. Cosmological issues related to decoherence are discussed, not only within the standard Friedmann cosmology, but also using the elements of the theory of black holes, wormholes and strings. The relations between the formalism of consistent histories defined in terms of decoherence functionals and the environmental decoherence are discussed in chapter 5, also written by Kiefer. The Feynman--Vernon influence functional for the quantum open system is presented in detail as the first example of decoherence functional. Then the general theory is outlined together with possible interpretations including cosmological aspects. The next chapter by Giulini presents an overview of the superselection rules arising from physical symmetries and gauge transformations both for nonrelativistic quantum mechanics and quantum field theory. Critical discussion of kinematical superselection rules versus dynamical ones is illustrated by numerous examples like Galilei invariant quantum mechanics, quantum electrodynamics and quantum gravity. The introduction to the theory of quantum open systems and its applications to decoherence models is given in chapter 7 by Kupsch. Generalized master equations, Markovian approximation and a few Hamiltonian models relevant for decoherence are discussed. Some mathematical tools, e.g., complete positivity and entropy inequalities are also presented. The last chapter by Stamatescu is devoted to stochastic collapse models which can be interpreted either as certain representations of the dynamics of open quantum systems or as fundamental modifications of the Schr\"odinger equation. The final part of the book consists of remarks by Zeh on related concepts and methods and seven appendices. The broad spectrum, mathematically-friendly presentation, inclusion of the very recent developments and the extensive bibliography (about 550 references) make this book a valuable reference for all researchers, graduate and PhD students interested in the foundations of quantum mechanics, quantum open systems and quantum information. The relative independence of the chapters and numerous redundancies allow for selective reading, which is very helpful for newcomers to this field.