Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1603.09499

Classicality in Quantum Mechanics: model for pointer states and decoherence

Kentaro Urasaki

Published Mar 31, 2016• 0 citations
arXivHTMLPDF

Abstract

We have studied the emergence of classical states in the perturbative interaction model. The states which interact with many other degrees of freedom, such as the center of mass of a macro-object, play important role. Although the random phase mechanism is effective as same as Zurek's strong correlation model, there are enormous states, each of which independently developes due to the orthogonality of the environmental states. In these privileged states, the subsystem picture with the separability is stable.

DOI
10.48550/arxiv.1603.09499

Related papers

Pointer States and Decoherence in Quantum Unitarity: Energy Conservation for Weak Interaction Model

Kentaro Urasaki

The purpose of the present paper is to derive the pointer states of a macro-object using a simple perturbation method. We study the model Hamiltonian involving the weak interaction between the center of mass and its environment. The main conclusion is that the pointer states emerge as the small part of the total state vector when the interaction Hamiltonian is not dominant: the degrees of freedom being at the center of interaction can be localized. In the weak interaction case, if the disappearance of the energy contribution from the off-diagonal terms is caused by the decoherence, it threatens the conservation law. In this study, however, the energy conservation reasonably holds, since the non-classical (i.e., normal quantum) states give main contribution to it. The emergence of the pointer states also implies the special initial state in which the localized state makes the deep well of the potential. In the result, the unitary time evolution of a pointer state is very different from that of the majority of the original state vector of the total system.

arXiv:1610.06066•Oct 19, 2016•0 citations

A General Derivation of Pointer States: Decoherence and Classicality

Kentaro Urasaki

The purpose of the present study is to derive the pointer states of a macroscopic system interacting with its environment, under the general assumptions, i.e., without assuming any form of the interaction Hamiltonian. The lowest order perturbation leads that the interaction energy shifts the phase factors of the state vectors. For a macroscopic system, these factors are the macroscopic quantities even for the very weak interaction. When we group the state vector of the total system by the view point of environmental side, the destructive interference occurs and the stationary phase approximation can be adopted. Only the pointer states then survive and the decoherence also occurs. The present approach is within the standard quantum mechanics as same as the standard decoherence theory, but the meaning of the classical state is much clear.

arXiv:1404.4457•Apr 17, 2014•0 citations

Classical selection and quantum Darwinism

Ruth E. Kastner

This short letter in response to Wojciech Zurek’s article “Quantum Darwinism, classical reality, and the randomness of quantum jumps” points out extant rebuttals in the literature to some of the author’s key claims.On the first page of his arXiv.org version of the Physics Today article (http://arxiv.org/abs/1412.5206), Zurek states thatdecoherence selects preferred pointer states that survive interaction with the environment. They are localized and effectively classical. They persist while their superpositions decohere. Decoherence marks the border between quantum and classical, alleviating concern about flagrant … manifestations of quantumness in the macroscopic domain.Here we consider emergence of “the classical” starting at a more fundamental pre-decoherence level, tracing the origin of preferred pointer states.However, the idea that preferred pointer states naturally “emerge” from the quantum level has been refuted in the literature, in particular in a paper11. R. E. Kastner, Stud. Hist. Philos. Mod. Phys. 48, 56 (2014), and references therein. https://doi.org/10.1016/j.shpsb.2014.06.004 showing that “classical” pointer states do not emerge unless a key aspect of classicality has been tacitly assumed from the beginning. In other words, the “quantum Darwinism” program is fatally circular.The assumption generating the circularity usually takes the form of a predesignated system that is considered separable from its environment (the same assumption appears in the discussion about information flow in Zurek’s article). The system acquires decohered observable (or stable) states because it is presumed to be distinguishable from a designated set of environmental subsystems, all assumed as having random phases—with respect to each other and the system. The only correlations between the system and the environmental subsystems are assumed to be established via the designated Hamiltonians.However, in the absence of this sort of predesignated partitioning of all degrees of freedom into the system and its surroundings—measurement apparatus, environment, and so forth—where the initial phase of each subsystem is random, the desired decoherence and emergence of pointer states, or einselection, do not follow. The partitioning is inevitably based on what a human observer would be able to identify and measure, such as distinguishable atoms and molecules, so the account is dependent on assuming the classical realm of the observer.The need for this pre-partitioning fatally conflicts with the claim that classicality emerges naturally from the quantum realm: Absent a pre-partitioning of all degrees of freedom into uncorrelated systems of interest, classical pointer states do not emerge. With unitary-only dynamics (lacking nonunitary collapse), the quantum realm does not have any a priori preference for the assumed uncorrelated degrees of freedom. On the contrary, a unitary-only evolution would typically begin with a maximally entangled universal state.As I noted in reference 11. R. E. Kastner, Stud. Hist. Philos. Mod. Phys. 48, 56 (2014), and references therein. https://doi.org/10.1016/j.shpsb.2014.06.004, one can observe the decoherence process experimentally, but that observation does not demonstrate that einselection occurs in a unitary-only dynamics or that classicality emerges in such a dynamics. A key missing ingredient in quantum Darwinism is some real physical randomization process, such as collapse, that could create an observer-independent, physical partitioning at the quantum level. Without such a process, quantum Darwinism contains the same kind of logical circularity as Boltzmann’s H-theorem, which attempted to derive irreversible thermodynamic laws from reversible laws. Boltzmann inadvertently smuggled in irreversibility by assuming molecular chaos; quantum Darwinists smuggle in classicality via their partitioning of the universe into distinguishable systems of interest that interact with mutually randomized environmental subsystems.In his article, Zurek does not address this refutation of quantum Darwinism and repeats the refuted claims and circular assumptions. Similar criticisms of quantum Darwinism’s presumption of classically distinguishable primordial systems, raised by Jasmina Jeknić-Dugić, Miroljub Dugić, and collaborators,2–42. J. Jeknić-Dugić, M. Dugić, A. Francom, Int. J. Theor. Phys. 53, 169 (2014). https://doi.org/10.1007/s10773-013-1794-x3. J. Jeknić-Dugić, M. Dugić, A. Francom, M. Arsenijević, Open Access Libr. J. 1, e501 (2014). https://doi.org/10.4236/oalib.11005014. M. Dugić, J. Jeknić, Int. J. Theor. Phys. 45, 2215 (2006). https://doi.org/10.1007/s10773-006-9186-0 and Chris Fields’s concern about the division of primordial degrees of freedom into a classically distinguishable system and environment55. C. Fields, Phys. Essays 24, 518 (2011). https://doi.org/10.4006/1.3644391 have also not been countered by proponents of quantum Darwinism.I acknowledge and thank Miroljub Dugić for his helpful comments.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. R. E. Kastner, Stud. Hist. Philos. Mod. Phys. 48, 56 (2014), and references therein. https://doi.org/10.1016/j.shpsb.2014.06.004, Google ScholarCrossref2. J. Jeknić-Dugić, M. Dugić, A. Francom, Int. J. Theor. Phys. 53, 169 (2014). https://doi.org/10.1007/s10773-013-1794-x, Google ScholarCrossref3. J. Jeknić-Dugić, M. Dugić, A. Francom, M. Arsenijević, Open Access Libr. J. 1, e501 (2014). https://doi.org/10.4236/oalib.1100501, Google ScholarCrossref4. M. Dugić, J. Jeknić, Int. J. Theor. Phys. 45, 2215 (2006). https://doi.org/10.1007/s10773-006-9186-0, Google ScholarCrossref5. C. Fields, Phys. Essays 24, 518 (2011). https://doi.org/10.4006/1.3644391, Google ScholarCrossref© 2015 American Institute of Physics.

Physics Today•Apr 30, 2015•3 citations

Decoherence, einselection and the existential interpretation (the rough guide)

Wojciech Hubert Zurek

The roles of decoherence and environment–induced superselection in the emergence of the classical from the quantum substrate are described. The stability of correlations between the einselected quantum pointer states and the environment allows them to exist almost as objectively as classical states were once thought to exist: there are ways of finding out what is the pointer state of the system which uses redundancy of their correlations with the environment, and which leave einselected states essentially unperturbed. This relatively objective existence of certain quantum states facilitates operational definition of probabilities in the quantum setting. Moreover, once there are states that ‘exist’and can be ‘found out’, a ‘collapse’ in the traditional sense is no longer necessary—–in effect, it has already happened. The records of the observer will contain evidence of an effective collapse. The role of the preferred states in the processing and storage of information is emphasized. The existential interpretation based on the relatively objective existence of stable correlations between the einselected states of observers memory and in the outside universe is formulated and discussed.

arXiv:quant-ph/9805065•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Aug 15, 1998•215 citations

Decoherence, einselection, and the quantum origins of the classical

Wojciech Hubert Zurek

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.

arXiv:quant-ph/0105127•Reviews of Modern Physics•May 22, 2003•4,294 citations

Classical dynamics emerging from quantum dynamics in macroscopic bodies, a note with a simple example

Vı́ctor Romero-Rochı́n

Using very general and well established ideas of the statistical physics of macroscopic bodies, that is, of those composed of many degrees of freedom, we show how classical behavior of the center of mass motion arises from a fully quantum mechanical description of the dynamics of the whole body. We do not attempt to provide a rigorous proof of the latter statement, but rather, we show or, at least, indicate the hypotheses needed to obtain the purported result. Moreover, we neither attempt to deal with the "most general" physical situation and, instead, we concentrate on a stylized model of a small solid, yet macroscopic, that we shall call a "little stone". The main hypothesis is that a macroscopic body can be decomposed into several smaller pieces, still macroscopic, that become statistically independent due to the short-range interaction nature of their constituent atoms. The ensuing main result is that the quantum distributions of extensive variables of the body become sharply-peaked. The center of mass variables are of this type and hence their dynamics is essentially classical. We point out the crucial role played by the external potential, in which the motion occurs, as the macroscopic agent that executes the "measurement" process of the center of mass.

arXiv:1504.05065•Apr 20, 2015•0 citations
We have studied the emergence of classical states in the perturbative interaction model. The states which interact with many other degrees of freedom, such as the center of mass of a macro-object, play important role. Although the random phase mechanism is effective as same as Zurek's strong correlation model, there are enormous states, each of which independently developes due to the orthogonality of the environmental states. In these privileged states, the subsystem picture with the separability is stable.
The purpose of the present paper is to derive the pointer states of a macro-object using a simple perturbation method. We study the model Hamiltonian involving the weak interaction between the center of mass and its environment. The main conclusion is that the pointer states emerge as the small part of the total state vector when the interaction Hamiltonian is not dominant: the degrees of freedom being at the center of interaction can be localized. In the weak interaction case, if the disappearance of the energy contribution from the off-diagonal terms is caused by the decoherence, it threatens the conservation law. In this study, however, the energy conservation reasonably holds, since the non-classical (i.e., normal quantum) states give main contribution to it. The emergence of the pointer states also implies the special initial state in which the localized state makes the deep well of the potential. In the result, the unitary time evolution of a pointer state is very different from that of the majority of the original state vector of the total system.
The purpose of the present study is to derive the pointer states of a macroscopic system interacting with its environment, under the general assumptions, i.e., without assuming any form of the interaction Hamiltonian. The lowest order perturbation leads that the interaction energy shifts the phase factors of the state vectors. For a macroscopic system, these factors are the macroscopic quantities even for the very weak interaction. When we group the state vector of the total system by the view point of environmental side, the destructive interference occurs and the stationary phase approximation can be adopted. Only the pointer states then survive and the decoherence also occurs. The present approach is within the standard quantum mechanics as same as the standard decoherence theory, but the meaning of the classical state is much clear.
This short letter in response to Wojciech Zurek’s article “Quantum Darwinism, classical reality, and the randomness of quantum jumps” points out extant rebuttals in the literature to some of the author’s key claims.On the first page of his arXiv.org version of the Physics Today article (http://arxiv.org/abs/1412.5206), Zurek states thatdecoherence selects preferred pointer states that survive interaction with the environment. They are localized and effectively classical. They persist while their superpositions decohere. Decoherence marks the border between quantum and classical, alleviating concern about flagrant … manifestations of quantumness in the macroscopic domain.Here we consider emergence of “the classical” starting at a more fundamental pre-decoherence level, tracing the origin of preferred pointer states.However, the idea that preferred pointer states naturally “emerge” from the quantum level has been refuted in the literature, in particular in a paper11. R. E. Kastner, Stud. Hist. Philos. Mod. Phys. 48, 56 (2014), and references therein. https://doi.org/10.1016/j.shpsb.2014.06.004 showing that “classical” pointer states do not emerge unless a key aspect of classicality has been tacitly assumed from the beginning. In other words, the “quantum Darwinism” program is fatally circular.The assumption generating the circularity usually takes the form of a predesignated system that is considered separable from its environment (the same assumption appears in the discussion about information flow in Zurek’s article). The system acquires decohered observable (or stable) states because it is presumed to be distinguishable from a designated set of environmental subsystems, all assumed as having random phases—with respect to each other and the system. The only correlations between the system and the environmental subsystems are assumed to be established via the designated Hamiltonians.However, in the absence of this sort of predesignated partitioning of all degrees of freedom into the system and its surroundings—measurement apparatus, environment, and so forth—where the initial phase of each subsystem is random, the desired decoherence and emergence of pointer states, or einselection, do not follow. The partitioning is inevitably based on what a human observer would be able to identify and measure, such as distinguishable atoms and molecules, so the account is dependent on assuming the classical realm of the observer.The need for this pre-partitioning fatally conflicts with the claim that classicality emerges naturally from the quantum realm: Absent a pre-partitioning of all degrees of freedom into uncorrelated systems of interest, classical pointer states do not emerge. With unitary-only dynamics (lacking nonunitary collapse), the quantum realm does not have any a priori preference for the assumed uncorrelated degrees of freedom. On the contrary, a unitary-only evolution would typically begin with a maximally entangled universal state.As I noted in reference 11. R. E. Kastner, Stud. Hist. Philos. Mod. Phys. 48, 56 (2014), and references therein. https://doi.org/10.1016/j.shpsb.2014.06.004, one can observe the decoherence process experimentally, but that observation does not demonstrate that einselection occurs in a unitary-only dynamics or that classicality emerges in such a dynamics. A key missing ingredient in quantum Darwinism is some real physical randomization process, such as collapse, that could create an observer-independent, physical partitioning at the quantum level. Without such a process, quantum Darwinism contains the same kind of logical circularity as Boltzmann’s H-theorem, which attempted to derive irreversible thermodynamic laws from reversible laws. Boltzmann inadvertently smuggled in irreversibility by assuming molecular chaos; quantum Darwinists smuggle in classicality via their partitioning of the universe into distinguishable systems of interest that interact with mutually randomized environmental subsystems.In his article, Zurek does not address this refutation of quantum Darwinism and repeats the refuted claims and circular assumptions. Similar criticisms of quantum Darwinism’s presumption of classically distinguishable primordial systems, raised by Jasmina Jeknić-Dugić, Miroljub Dugić, and collaborators,2–42. J. Jeknić-Dugić, M. Dugić, A. Francom, Int. J. Theor. Phys. 53, 169 (2014). https://doi.org/10.1007/s10773-013-1794-x3. J. Jeknić-Dugić, M. Dugić, A. Francom, M. Arsenijević, Open Access Libr. J. 1, e501 (2014). https://doi.org/10.4236/oalib.11005014. M. Dugić, J. Jeknić, Int. J. Theor. Phys. 45, 2215 (2006). https://doi.org/10.1007/s10773-006-9186-0 and Chris Fields’s concern about the division of primordial degrees of freedom into a classically distinguishable system and environment55. C. Fields, Phys. Essays 24, 518 (2011). https://doi.org/10.4006/1.3644391 have also not been countered by proponents of quantum Darwinism.I acknowledge and thank Miroljub Dugić for his helpful comments.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. R. E. Kastner, Stud. Hist. Philos. Mod. Phys. 48, 56 (2014), and references therein. https://doi.org/10.1016/j.shpsb.2014.06.004, Google ScholarCrossref2. J. Jeknić-Dugić, M. Dugić, A. Francom, Int. J. Theor. Phys. 53, 169 (2014). https://doi.org/10.1007/s10773-013-1794-x, Google ScholarCrossref3. J. Jeknić-Dugić, M. Dugić, A. Francom, M. Arsenijević, Open Access Libr. J. 1, e501 (2014). https://doi.org/10.4236/oalib.1100501, Google ScholarCrossref4. M. Dugić, J. Jeknić, Int. J. Theor. Phys. 45, 2215 (2006). https://doi.org/10.1007/s10773-006-9186-0, Google ScholarCrossref5. C. Fields, Phys. Essays 24, 518 (2011). https://doi.org/10.4006/1.3644391, Google ScholarCrossref© 2015 American Institute of Physics.
The roles of decoherence and environment–induced superselection in the emergence of the classical from the quantum substrate are described. The stability of correlations between the einselected quantum pointer states and the environment allows them to exist almost as objectively as classical states were once thought to exist: there are ways of finding out what is the pointer state of the system which uses redundancy of their correlations with the environment, and which leave einselected states essentially unperturbed. This relatively objective existence of certain quantum states facilitates operational definition of probabilities in the quantum setting. Moreover, once there are states that ‘exist’and can be ‘found out’, a ‘collapse’ in the traditional sense is no longer necessary—–in effect, it has already happened. The records of the observer will contain evidence of an effective collapse. The role of the preferred states in the processing and storage of information is emphasized. The existential interpretation based on the relatively objective existence of stable correlations between the einselected states of observers memory and in the outside universe is formulated and discussed.
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.
Using very general and well established ideas of the statistical physics of macroscopic bodies, that is, of those composed of many degrees of freedom, we show how classical behavior of the center of mass motion arises from a fully quantum mechanical description of the dynamics of the whole body. We do not attempt to provide a rigorous proof of the latter statement, but rather, we show or, at least, indicate the hypotheses needed to obtain the purported result. Moreover, we neither attempt to deal with the "most general" physical situation and, instead, we concentrate on a stylized model of a small solid, yet macroscopic, that we shall call a "little stone". The main hypothesis is that a macroscopic body can be decomposed into several smaller pieces, still macroscopic, that become statistically independent due to the short-range interaction nature of their constituent atoms. The ensuing main result is that the quantum distributions of extensive variables of the body become sharply-peaked. The center of mass variables are of this type and hence their dynamics is essentially classical. We point out the crucial role played by the external potential, in which the motion occurs, as the macroscopic agent that executes the "measurement" process of the center of mass.