Decoherence is always an approximate notion.Complete decoherence is impossible.Indeed, if we wait a very long time, decoherence will always be reversed, as the information needed to define superpositions seeps back into the system from the environment. . . .Decoherence is a statistical process, similar to the random motion of atoms that leads to increases of entropy, bringing systems to equilibrium.These pro cesses appear to be irreversible.But they are actually reversible. . . .The second law of thermodynamics, according to which entropy probably increases, can hold only for times much shorter than the Poincaré recurrence time.If we wait long enough, we will see entropy go down as often as it goes up. -Lee Smolin (2019, 101)The truth of quantum real ity is an ambiguous truth.It calls upon us to live with the possibility of other possibilities.But such ambiguity can be creative.Selforganizing quantum systems thrive on ambiguity. . . .If a self-organizing system becomes too static, it runs down; if it becomes too chaotic it breaks apart.It needs a creative balance of order and chaos to thrive.This is ambiguity.-Danah Zohar and Ian Marshall (1994, 159) Pillars and CementThe idea we develop here is that the quantum ecol ogy is characterized by three interdependent pillars-uncertainty, entanglement, and discreteness, as foundational aspects of quantum physics-that come to define a selforganizing world-sensing cemented together or, better, enacted through embodiment, which, in turn, operationalizes a synthetic operating system deeply disruptive of today's scenario.Speaking of "observership," Hertog (2023, 142) writes that this act is "an agency operating at a deeper level, an indispensable part of the continual process through which physical 5 Ecol ogy: A Pos si ble Quantum-Based Paradigm
Decoherence is always an approximate notion.Complete decoherence is impossible.Indeed, if we wait a very long time, decoherence will always be reversed, as the information needed to define superpositions seeps back into the system from the environment. . . .Decoherence is a statistical process, similar to the random motion of atoms that leads to increases of entropy, bringing systems to equilibrium.These pro cesses appear to be irreversible.But they are actually reversible. . . .The second law of thermodynamics, according to which entropy probably increases, can hold only for times much shorter than the Poincaré recurrence time.If we wait long enough, we will see entropy go down as often as it goes up. -Lee Smolin (2019, 101)The truth of quantum real ity is an ambiguous truth.It calls upon us to live with the possibility of other possibilities.But such ambiguity can be creative.Selforganizing quantum systems thrive on ambiguity. . . .If a self-organizing system becomes too static, it runs down; if it becomes too chaotic it breaks apart.It needs a creative balance of order and chaos to thrive.This is ambiguity.-Danah Zohar and Ian Marshall (1994, 159) Pillars and CementThe idea we develop here is that the quantum ecol ogy is characterized by three interdependent pillars-uncertainty, entanglement, and discreteness, as foundational aspects of quantum physics-that come to define a selforganizing world-sensing cemented together or, better, enacted through embodiment, which, in turn, operationalizes a synthetic operating system deeply disruptive of today's scenario.Speaking of "observership," Hertog (2023, 142) writes that this act is "an agency operating at a deeper level, an indispensable part of the continual process through which physical 5 Ecol ogy: A Pos si ble Quantum-Based Paradigm
We are in the midst of a renaissance in the study and interpretation of fundamental quantum mechanics, from quantum coherence and quantum entanglement to the quantum measurement process. This stems partly from the impressive advances in experimental techniques that are making yesterday's gedanken experiment today's reality. Another reason quantum coherence and entanglement have come to the forefront is the emerging and tantalizing field of quantum information science. The ability to store information in quantum systems may someday yield devices that process quantum superpositions of inputs in parallel or improve communication through the `wiring' implicit in quantum entanglement. Indeed, quantum computing has the remote prospect of revolutionizing the way we store and process information. This has become particularly important in the face of impending limits on the miniaturization of conventional computers due to quantum effects. Of course, all real systems face limits imposed by decoherence, or the environmentally-induced destruction of quantum coherence. Here, superpositions of quantum states suddenly become probabilistic mixtures of states when they interact with the environment or when the system parameters are fluctuating. Decoherence theory is commonly interpreted as a way to quantify the elusive boundary between quantum and classical worlds and almost always precludes the existence of complex quantum superpositions, except at extremely short time scales. In practice, it is very important to study how decoherence appears in particular quantum systems and try to fight against it. In this special issue of Journal of Optics B: Quantum and Semiclassical Optics , we highlight recent results in the exciting area of quantum coherence and entanglement, including generating interesting and complex quantum states, characterizing coherence and entanglement in these systems, and triumphing over relevant decoherence processes. We hope this issue will not only act as a bookmark in the ongoing study of fundamental quantum mechanics, but will also help guide the rapid developments in quantum information science.
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.
Decoherence is the physical process by which the classical world - the world of common sense - emerges from its quantum underpinnings. This physical process refers to the loss of phase coherence between the parts of a quantum system, because of the interaction of the system with the environment. This text with contributions from the Advanced Research Workshop (ARW) provides an in-depth discussion of this physical process and of its relevance in understanding and interpreting quantum mechanics, with special emphasis given to its implications in implementing the practical aspects of quantum computation and information transfer. The ARW brings together scientists in diverse fields such as mathematical physics, quantum logic, and quantum computing for an intense, interdisciplinary discussion of decoherence and its practical implications in quantum computing. Quantum computing represents possibly the epitome of the technological impact that quantum mechanics can have on technological developments in the foreseeable future. Its realization would allow the performance of tasks that are practically unthinkable in terms of classical physics. Such exotic occurrences as breaking hitherto unbreakable codes, searching enormous lists for specific entries, and communicating with messages that betray the presence of eavesdropping would fall within reach. These wonders are possible when one exploits the logical consequences of the laws that govern natural phenomena at the most fundamental level, namely, the laws of quantum mechanics standing squarely in the way of these developments is decoherence. The aim of the workshop was to provide an in-depth discussion of the state of affairs regarding the progress that is being made in understanding the effects of decoherence in quantum computation and information transfer and in getting around it. The present is a particularly fitting time for discussions of an interdisciplinary nature, encompassing quantum logic, mathematics and physics, addressing these issues. The invited speakers have been chosen among those who continue to make significant contributions in this domain of science and we expect lively and informative presentations and discussions. Also invited were those who are expected to benefit greatly from exposure to the issues under consideration and who will carry developments further as their own scientific career unfolds.
Recently, the possibility of investigating single molecule, or single spin observables, as well as the necessity of a better understanding of the mechanisms underlying quantum dynamics in order to obtain nanoscale devices and nanostructered materials suitable for quantum computing tasks, have revived the interest in foundational aspects of quantum statistical mechanics. This thesis aims to give a contribution to this field by re-considering the statistical characterization of a quantum system at the light of some paradigmatic changes in our understanding of quantum theory which have taken place in the last two decades. In particular the impressive development of quantum information theory has changed the perceptions of quantum entanglement: for a long time it has been considered a somewhat paradoxical property of the matter at the atomic scale, but now it is regarded as an essential and ubiquitous phenomenon whose consequences are affecting the very macroscopic world that we experience. Still the decoherence program has brought out the importance of considering a quantum system together with its environment in order to clarify some key aspects of quantum dynamics. Thus, we start from the idea that quantum correlations are ubiquitous and somewhat uncontrollable in systems with many degrees of freedom which are typically considered in statistical mechanics. As a consequence we assume the standpoint that quantum statistical mechanics has not to be based on the underlying idea of a collection of many, independent quantum systems but rather it has to emerge at the level of a global wavefunction (pure state) which describes the system as well as its environment as a whole. In order to investigate the consequences of these assumptions we study the equilibrium distribution of an isolated quantum system. This is defined, in analogy with the ergodic foundations of classical statistical mechanics, on the basis of the time evolution of the quantum state. Then, we study the emergence of thermodynamic properties in a quantum system by studying the probability distribution of some function of interests, as the entropy and the equilibrium state of a subsystem, on Ensembles of Pure States. Such a probability distribution is derived from the geometry of the Hilbert space, and the theoretical tools suitable for its characterization are developed. On the one hand we perform a numerical sampling of the ensemble distributions by employing Monte Carlo techniques, on the other hand simpler analytical approximation of the geometrical distributions are derived by means of a maximum entropy principle. Model systems composed of an ensemble of spins are chosen to illustrate the salient features which emerge from the developed theoretical framework: the main point is that the Ensemble Distributions of “thermodynamic observables” (entropy or equilibrium state of a subsystem) are sharply peaked around a typical value. From the analysis it emerges that each of the overwhelming majority of the wavefunctions which has appreciable weight in the considered ensemble, is characterized by the same value of the “macroscopic” functions. This is a striking evidence of the “typicality” of these properties. In the essence, our impossibility to know the state of the system in detail does not matter, just for the remarkable fact that almost all quantum states behave essentially in the same way. By virtue of this typicality the study of the behaviour of the typical values of the thermodynamic function become meaningful. Notably, under certain conditions, one recovers the results of standard statistical mechanics, that is, the equilibrium average of the state of a subsystem can be cast in the Boltzmann canonical form at the temperature given by the usual thermodynamical relation . In the second part of the thesis we consider the dynamical aspects of the equilibrium state of a subsystem interacting with its environment. The fluctuations around the equilibrium average critically depends on the entanglement between the system and the environment and on the form of the interaction Hamiltonian. The connection between the dynamics of the fluctuations of an observable at the equilibrium and the relaxation toward the equilibrium from a “non typical” initial value is also investigated with the aid of simple model systems. The study presented in this thesis was partly motivated by a critical analysis of the statistical methods available for the theoretical modelling of magnetic resonance experiments. One of these, the Stochastic Liouville Equation, has been employed in a work completed during the first year of my Ph.D. program in order to interpret some feature of a two dimensional electron spin resonance experiment, [Fresch B., Frezzato D., Moro G. J., Kothe G., Freed J. H.; J. Phys. Chem. B., 110, 24238, (2006)].