Abstract The purpose of this article, which is our contribution to Wolfgang Schleich’s Festschrift, is to present an unconventional perspective of two fundamental, interrelated problems: the emergence of classicality and the observer’s role in quantum mechanics. In our perspective, the decoherence of quantum states of a system or its measuring device (meter) by the environment cannot replace the role of the observer, nor can it provide the ultimate explanation of the transition of the system from quantumness to classicality. The reason is that decoherence, despite appearances, typically does not irretrievably obliterate the information on the system’s state. Even in cases where the environment has the potential of erasing this information, the observer can negate decoherence effects in the meter or the system by dynamical control. We contend that the choice of measuring bases and observables is largely up to the controller-observer (CO) that need not possess unlimited resources in order to steer or freeze ( at will ) the system-state evolution and its quantumness, notwithstanding the environment effects. An analogy is drawn between the outlined approach and Lamarckism, the theory of evolution that preceded Darwinism. Quantum Lamarckism expresses our view of evolution as functional adaptation of the system to the interplay between environmental and CO effects . In our view, both conceptually and practically, decoherence may be deemed non-essential for determining the evolution of a quantum system embedded in its environment, provided the CO has an adequate, albeit limited, arsenal of resources.
Abstract The purpose of this article, which is our contribution to Wolfgang Schleich’s Festschrift, is to present an unconventional perspective of two fundamental, interrelated problems: the emergence of classicality and the observer’s role in quantum mechanics. In our perspective, the decoherence of quantum states of a system or its measuring device (meter) by the environment cannot replace the role of the observer, nor can it provide the ultimate explanation of the transition of the system from quantumness to classicality. The reason is that decoherence, despite appearances, typically does not irretrievably obliterate the information on the system’s state. Even in cases where the environment has the potential of erasing this information, the observer can negate decoherence effects in the meter or the system by dynamical control. We contend that the choice of measuring bases and observables is largely up to the controller-observer (CO) that need not possess unlimited resources in order to steer or freeze ( at will ) the system-state evolution and its quantumness, notwithstanding the environment effects. An analogy is drawn between the outlined approach and Lamarckism, the theory of evolution that preceded Darwinism. Quantum Lamarckism expresses our view of evolution as functional adaptation of the system to the interplay between environmental and CO effects . In our view, both conceptually and practically, decoherence may be deemed non-essential for determining the evolution of a quantum system embedded in its environment, provided the CO has an adequate, albeit limited, arsenal of resources.
The consensus regarding quantum measurements rests on two statements: (i) von Neumann’s standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the “meter”) unambiguously determines the measuring (“pointer”) basis. The latter statement means that the environment monitors (measures) selected observables of the meter and (indirectly) of the system. Equivalently, a measured quantum state must end up in one of the “pointer states” that persist in the presence of the environment. We find that, unless we restrict ourselves to projective measurements, decoherence does not necessarily determine the pointer basis of the meter. Namely, generalized measurements commonly allow the observer to choose from a multitude of alternative pointer bases that provide the same information on the observables, regardless of decoherence. By contrast, the measured observable does not depend on the pointer basis, whether in the presence or in the absence of decoherence. These results grant further support to our notion of Quantum Lamarckism, whereby the observer’s choices play an indispensable role in quantum mechanics.
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.
This study offers a comprehensive technical analysis of the mechanisms through which classical behavior emerges from the dynamics of quantum measurement. Beginning with unitary evolution and the principles of measurement, we construct the framework of environment-induced decoherence, the selection of pointer states, and the reduction of interference. Our examination focuses on how effective classicality emerges through reduced density matrices, quantum Darwinism, and consistent histories, highlighting the importance of system-environment interactions in determining stable observables. The review investigates into mathematical constructs such as spectral theory, completely positive maps, and quantum trajectories, linking them to experimental observations in mesoscopic systems, optomechanics, and superconducting circuits. We explore the constraints of decoherence in addressing the outcome problem and review interpretational models that tackle the remaining issues. The discussion emphasizes applications in quantum information, metrology, and tests of macroscopic superpositions. The article favors physical insights and mathematical guidance over exhaustive proofs, making it suitable for researchers in quantum foundations and quantum technologies.
Decoherence is traditionally viewed as a purely destructive process in quantum mechanics, primarily responsible for the loss of quantum information. However, this paper proposes and investigates a novel perspective: that decoherence can exhibit non-linear effects, significantly impacting the dynamical evolution of quantum systems. We construct a comprehensive quantum decoherence model, analyzing the intricate interactions between the decoherence process and the system's dynamics. Our analysis reveals the emergence of non-linear behavior during decoherence, providing a deeper understanding of the mechanism. Furthermore, we propose strategies for controlling these non-linear effects. The core claim of this paper is that decoherence is not merely a destructive mechanism, but a dynamic one capable of producing non-linear phenomena. This research offers a fundamental shift in the comprehension of decoherence's role and consequences within quantum systems.
The manner in which states of some quantum systems become effectively classical is of great significance for the foundations of quantum physics, as well as for problems of practical interest such as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ``Schr\"odinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ``collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ``classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ``found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ``fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.
At present there is a consensus about the fact that the emergence of the classical world from the underlying quantum reality involves the physical phenomenon of decoherence, which is usually studied in the version proposed by Zurek and his collaborators. According to this version, decoherence is a process resulting from the interaction between a quantum system and its environment (environment-induced decoherence, EID); this process singles out the observables that receive definite classical values. The aim of this paper is to propose a top-down approach to decoherence, which takes the perspective of the whole closed system, and considers whether each set of degrees of freedom decoheres or not. This approach is more general than the orthodox open-system perspective and dissolves some of its conceptual problems. Although decoherence becomes relative to the way in which the closed system is decomposed, the quantum-to-classical transition defines unequivocally the realm of classicality by identifying the observables with classical-like behavior.