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Random Unitary Operations and Quantum Darwinism

Nenad Balanesković

Published Jan 1, 2016• 0 citations
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Abstract

We study the behavior of Quantum Darwinism (Zurek, Nature Physics 5, 181 - 188 (2009)) within the iterative, random unitary operations qubit-model of pure decoherence (Novotn´y et al, New Jour. Phys. 13, 053052 (2011)). We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system from the point of view of its environment, is not a generic phenomenon, but depends on the specific form of initial states and on the type of system-environment interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial initial states of environment that allow to store information about an open system of interest and its pointer-basis with maximal efficiency. Furthermore, we investigate the behavior of Quantum Darwinism after introducing dissipation into the iterative random unitary qubit model with pure decoherence in accord with V. Scarani et al (Phys. Rev. Lett. 88, 097905 (2002)) and reconstruct the corresponding dissipative attractor space. We conclude that in Zurek’s qubit model Quantum Darwinism depends on the order in which pure decoherence and dissipation act upon an initial state of the entire system. We show explicitly that introducing dissipation into the random unitary evolution model in general suppresses Quantum Darwinism (regardless of the order in which decoherence and dissipation are applied) for all positive non-zero values of the dissipation strength parameter, even for those initial state configurations which, in Zurek’s qubit model and in the random unitary model with pure decoherence, would lead to Quantum Darwinism. Finally, we discuss what happens with Quantum Darwinism after introducing into the iterative random unitary qubit model with pure decoherence (asymmetric) dissipation and dephasing, again in accord with V. Scarani et al (Phys. Rev. Lett. 88, 097905 (2002)), and reconstruct the corresponding dissipative-dephasing attractor space. We conclude that dephasing does not influence the dynamics of quantum systems in Zurek’s qubit model of Quantum Darwinism. Similarly, we see that also within the random unitary evolution dephasing does not alter or influence the (dis-)appearance of Quantum Darwinism: i.e. the random unitary evolution of a quantum state governed by the quantum operation enclosing pure decoherence, dissipation and dephasing is in the asymptotic limit of many iterations significantly determined by the interplay between pure decoherence and dissipation, whereas the dephasing part of the random unitary evolution does not contribute to the corresponding asymptotic attractor space of the random unitary iteration.

DOI
10.26083/tuprints-00005148

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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

Attractor spaces of dissipative dephased random unitary evolution and quantum Darwinism

Nenad Balanesković

Journal of Astrophysics & Aerospace Technology•Jan 1, 2016•0 citations

Experimental Realization of Quantum Darwinism State on Quantum Computers

Rakesh Kumar Saini, Bikash K. Behera

It is well-known that decoherence is a crucial barrier in realizing various quantum information processing tasks; on the other hand, it plays a pivotal role in explaining how a quantum system's fragile state leads to the robust classical state. Zurek [Nat. Phys. 5, 181-188 (2009)] has developed the theory which successfully describes the emergence of classical objectivity of quantum system via decoherence, introduced by the environment. Here, we consider two systems for a model universe, in which the first system shows a random quantum state, and the other represents the environment. We take 2-, 3-, 4-, 5- and 6-qubit quantum circuits, where the system consists of one qubit and the rest qubits represent the environment qubits. We experimentally realize the Darwinism state constructed by this system's ensemble on two real devices, ibmq_athens and ibmq_16_melbourne. We then use the results to investigate quantum-classical correlation and the mutual information present between the system and the environment.

arXiv:2012.07562•Jan 1, 2020•0 citations

Classical selection and quantum Darwinism

Wojciech Hubert Zurek

Zurek replies: Repeatability is a textbook postulate—not mine, as the comment by Alexia Auffèves and Philippe Grangier suggests. However, I like the idea of a “context,” provided its origin is quantum. Using an ab initio classical apparatus (made out of quantum atoms!) to supply a context is inconsistent. The Copenhagen interpretation used it as an ingenious and successful ad hoc fix, but it cannot be a fundamental solution. The inability to delineate a quantum–classical boundary makes matters worse. Textbooks adopt such a “shut up and calculate” ploy to paper over the inconsistency of their axioms.Quantum Darwinism and decoherence favor quasi-classical pointer states, accessible indirectly to many observers via the imprints they deposit in the environment. Pointer states in turn depend on the quantum context provided by the environment. They emerge from a quantum substrate and supply context for the quantum states of microsystems.Quantum theory is universally valid. Quantum Darwinism and decoherence explain why macrosystems behave classically: Decoherence limits the validity of the quantum principle of superposition. Preferred states are a compromise between amplification, which calls for many copies of the original, and the no-cloning theorem. An unknown state can’t be cloned, but decoherence can amplify pointer states and disseminate information about them throughout the environment.Observers access only environment fragments, hence they extract only classical information. Quantum coherence, as explained in my article, is out of reach. Observers will agree about states communicated by environment fragments, but only data about pointer states can be shared.11. M. Zwolak, W. H. Zurek, Sci. Rep. 3, 1729 (2013); https://doi.org/10.1038/srep01729A. Streltsov, W. H. Zurek, Phys. Rev. Lett. 111, 040401 (2013). https://doi.org/10.1103/PhysRevLett.111.040401 Objective existence arises from epiontic—that is, epistemic and ontological—quantum states via the proliferation of information. Robust, quasi-classical branches and elusive information about them both emerge via amplification-like decoherence.Deducing the measurement postulates—Born’s rule and hermiticity of observables—from a simple, self-consistent credo is an advance. The assumptions, that states inhabit Hilbert space and evolve unitarily, should be judged by what follows from them and not by an intuitive appeal to classical prejudices. After all, counterintuitive assumptions—for example, that the speed of light is independent of an observer’s motion—have led to deep and valid consequences.The comment by Ruth Kastner states that phase randomness is key for decoherence and quantum Darwinism and that it is unlikely. Both are incorrect: Random phases between states are typical when phases can be defined. Moreover, random phases aren’t essential for decoherence; an outflow of information suffices. Indeed, standard models—for example, of quantum Brownian motion—often employ environments in equilibrium, for which phases are undefined and the question of their randomness is ill-posed. An initial correlation with the environment complicates calculations,22. L. D. Romero, J. P. Paz, Phys. Rev. A 55, 4070 (1997). https://doi.org/10.1103/PhysRevA.55.4070 but it does not eliminate decoherence. As difficulties encountered by quantum computing research show, decoherence is generic and hard to avoid.Quantum Darwinism requires more than decoherence; it relies on an environment that can store and communicate information. Solar radiation enables that,33. C. J. Riedel, W. H. Zurek, Phys. Rev. Lett. 105, 020404 (2010); https://doi.org/10.1103/PhysRevLett.105.020404New J. Phys. 13, 073038 (2011); https://doi.org/10.1088/1367-2630/13/7/073038M. Zwolak, C. J. Riedel, W. H. Zurek, Phys. Rev. Lett. 112, 140406 (2014). https://doi.org/10.1103/PhysRevLett.112.140406 since the Sun is a localized photon source. Quantum Darwinism is impossible in a completely equilibrated environment, whose subsystems cannot store information.The question of how to define systems is indeed of interest, and I have noted it before.44. W. H. Zurek, Phil. Trans. Roy. Soc. A 356, 1793 (1998); https://doi.org/10.1098/rsta.1998.0250Rev. Mod. Phys. 75, 715 (2003). https://doi.org/10.1103/RevModPhys.75.715 The answer must go beyond decoherence: What constitutes a system depends on interactions that make or break it; molecules, for example, would fall apart if atomic interactions weakened.There is no reason to complicate matters by making the definition of a system part of the measurement problem. Systems are there from the start—Schrödinger’s cat is obviously distinct from the nucleus that determines the cat’s fate—and their presence alone does not solve the problem. Indeed, the measurement problem disappears absent a system distinct from a measuring apparatus. Quantum evolution of a universe without parts is deterministic. There is no apparatus to record a definite outcome and so no need to talk about measurement outcomes: There is literally nothing to explain. Recognizing the role of the environment—as another system—is then natural in seeking answers.I am in good company when accused of the H-theorem “mistake.” Still, Ludwig Boltzmann dealt with the evolution of a many-body system that is classical and isolated. In that classical setting, probability was a fault of an observer ignorant of the system’s precise state. Boltzmann’s Stosszahlansatz postulates uncorrelated trajectories and is a way of representing that ignorance. Although the Boltzmann equation is useful, calling on Stosszahlansatz to prove the H-theorem—that is, the second law of thermodynamics—was suspect. Evolution is deterministic and reversible, so while observers’ ignorance may increase, microscopic entropy of the closed system cannot change. Moreover, the information and hence ignorance of observers is irrelevant for classical dynamics.As I show in my article, in our quantum world probabilities arise via entanglement. A single photon that escapes with information about the fate of Schrödinger’s cat is enough to decohere the cat’s state. An observer can never catch up with the photon, so reversibility of the equations of motion notwithstanding, information loss can be irreversible for prosaic yet compelling reasons. The resulting entropy production can be accounted for by decoherence.55. W. H. Zurek, J. P. Paz, Phys. Rev. Lett. 72, 2508 (1994). https://doi.org/10.1103/PhysRevLett.72.2508The whole measurement (or Schrödinger’s cat) setup starts far from equilibrium. Quantum Darwinism and decoherence show why, in such nonequilibrium multipartite settings, pointer states—and not their superpositions—survive and information about them is amplified and recorded in many copies by the environment. Both the nonequilibrium setting and the division of the universe into systems are needed to state the problem. When certain assumptions are needed to state the problem, surely they can be used to solve it.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. M. Zwolak, W. H. Zurek, Sci. Rep. 3, 1729 (2013); https://doi.org/10.1038/srep01729, Google ScholarCrossrefA. Streltsov, W. H. Zurek, Phys. Rev. Lett. 111, 040401 (2013). https://doi.org/10.1103/PhysRevLett.111.040401, , Google ScholarCrossref2. L. D. Romero, J. P. Paz, Phys. Rev. A 55, 4070 (1997). https://doi.org/10.1103/PhysRevA.55.4070, Google ScholarCrossref3. C. J. Riedel, W. H. Zurek, Phys. Rev. Lett. 105, 020404 (2010); https://doi.org/10.1103/PhysRevLett.105.020404, Google ScholarCrossrefNew J. Phys. 13, 073038 (2011); https://doi.org/10.1088/1367-2630/13/7/073038, , Google ScholarCrossrefM. Zwolak, C. J. Riedel, W. H. Zurek, Phys. Rev. Lett. 112, 140406 (2014). https://doi.org/10.1103/PhysRevLett.112.140406, , Google ScholarCrossref4. W. H. Zurek, Phil. Trans. Roy. Soc. A 356, 1793 (1998); https://doi.org/10.1098/rsta.1998.0250, Google ScholarCrossrefRev. Mod. Phys. 75, 715 (2003). https://doi.org/10.1103/RevModPhys.75.715, , Google ScholarCrossref5. W. H. Zurek, J. P. Paz, Phys. Rev. Lett. 72, 2508 (1994). https://doi.org/10.1103/PhysRevLett.72.2508, Google ScholarCrossref© 2015 American Institute of Physics.

Physics Today•Apr 30, 2015•9 citations

Models of decoherence with negative dephasing rate

A. Pernice, Julius Helm, Walter T. Strunz

We determine the total state dynamics of a dephasing open quantum system using the standard environment of harmonic oscillators. Of particular interest are random unitary approaches to the same reduced dynamics and system-environment correlations in the full model. Concentrating on a model with an at times negative dephasing rate, the issue of non-Markovianity will also be addressed. Crucially, given the quantum environment, the appearance of non-Markovian dynamics turns out to be accompanied by a loss of system-environment correlations. Depending on the initial purity of the qubit state, these system-environment correlations may be purely classical over the whole relevant time scale, or there may be intervals of genuine system-environment entanglement. In the latter case, we see no obvious relation between the build-up or decay of these quantum correlations and Non-Markovianity.

•Feb 20, 2012•2 citations

Dissipation, dephasing and quantum Darwinism in qubit systems with random unitary interactions

Nenad Balanesković, Marc Mendler

arXiv:1606.09366•The European Physical Journal D•Sep 1, 2016•17 citations
We study the behavior of Quantum Darwinism (Zurek, Nature Physics 5, 181 - 188 (2009)) within the iterative, random unitary operations qubit-model of pure decoherence (Novotn´y et al, New Jour. Phys. 13, 053052 (2011)). We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system from the point of view of its environment, is not a generic phenomenon, but depends on the specific form of initial states and on the type of system-environment interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial initial states of environment that allow to store information about an open system of interest and its pointer-basis with maximal efficiency. Furthermore, we investigate the behavior of Quantum Darwinism after introducing dissipation into the iterative random unitary qubit model with pure decoherence in accord with V. Scarani et al (Phys. Rev. Lett. 88, 097905 (2002)) and reconstruct the corresponding dissipative attractor space. We conclude that in Zurek’s qubit model Quantum Darwinism depends on the order in which pure decoherence and dissipation act upon an initial state of the entire system. We show explicitly that introducing dissipation into the random unitary evolution model in general suppresses Quantum Darwinism (regardless of the order in which decoherence and dissipation are applied) for all positive non-zero values of the dissipation strength parameter, even for those initial state configurations which, in Zurek’s qubit model and in the random unitary model with pure decoherence, would lead to Quantum Darwinism. Finally, we discuss what happens with Quantum Darwinism after introducing into the iterative random unitary qubit model with pure decoherence (asymmetric) dissipation and dephasing, again in accord with V. Scarani et al (Phys. Rev. Lett. 88, 097905 (2002)), and reconstruct the corresponding dissipative-dephasing attractor space. We conclude that dephasing does not influence the dynamics of quantum systems in Zurek’s qubit model of Quantum Darwinism. Similarly, we see that also within the random unitary evolution dephasing does not alter or influence the (dis-)appearance of Quantum Darwinism: i.e. the random unitary evolution of a quantum state governed by the quantum operation enclosing pure decoherence, dissipation and dephasing is in the asymptotic limit of many iterations significantly determined by the interplay between pure decoherence and dissipation, whereas the dephasing part of the random unitary evolution does not contribute to the corresponding asymptotic attractor space of the random unitary iteration.
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.
It is well-known that decoherence is a crucial barrier in realizing various quantum information processing tasks; on the other hand, it plays a pivotal role in explaining how a quantum system's fragile state leads to the robust classical state. Zurek [Nat. Phys. 5, 181-188 (2009)] has developed the theory which successfully describes the emergence of classical objectivity of quantum system via decoherence, introduced by the environment. Here, we consider two systems for a model universe, in which the first system shows a random quantum state, and the other represents the environment. We take 2-, 3-, 4-, 5- and 6-qubit quantum circuits, where the system consists of one qubit and the rest qubits represent the environment qubits. We experimentally realize the Darwinism state constructed by this system's ensemble on two real devices, ibmq_athens and ibmq_16_melbourne. We then use the results to investigate quantum-classical correlation and the mutual information present between the system and the environment.
Zurek replies: Repeatability is a textbook postulate—not mine, as the comment by Alexia Auffèves and Philippe Grangier suggests. However, I like the idea of a “context,” provided its origin is quantum. Using an ab initio classical apparatus (made out of quantum atoms!) to supply a context is inconsistent. The Copenhagen interpretation used it as an ingenious and successful ad hoc fix, but it cannot be a fundamental solution. The inability to delineate a quantum–classical boundary makes matters worse. Textbooks adopt such a “shut up and calculate” ploy to paper over the inconsistency of their axioms.Quantum Darwinism and decoherence favor quasi-classical pointer states, accessible indirectly to many observers via the imprints they deposit in the environment. Pointer states in turn depend on the quantum context provided by the environment. They emerge from a quantum substrate and supply context for the quantum states of microsystems.Quantum theory is universally valid. Quantum Darwinism and decoherence explain why macrosystems behave classically: Decoherence limits the validity of the quantum principle of superposition. Preferred states are a compromise between amplification, which calls for many copies of the original, and the no-cloning theorem. An unknown state can’t be cloned, but decoherence can amplify pointer states and disseminate information about them throughout the environment.Observers access only environment fragments, hence they extract only classical information. Quantum coherence, as explained in my article, is out of reach. Observers will agree about states communicated by environment fragments, but only data about pointer states can be shared.11. M. Zwolak, W. H. Zurek, Sci. Rep. 3, 1729 (2013); https://doi.org/10.1038/srep01729A. Streltsov, W. H. Zurek, Phys. Rev. Lett. 111, 040401 (2013). https://doi.org/10.1103/PhysRevLett.111.040401 Objective existence arises from epiontic—that is, epistemic and ontological—quantum states via the proliferation of information. Robust, quasi-classical branches and elusive information about them both emerge via amplification-like decoherence.Deducing the measurement postulates—Born’s rule and hermiticity of observables—from a simple, self-consistent credo is an advance. The assumptions, that states inhabit Hilbert space and evolve unitarily, should be judged by what follows from them and not by an intuitive appeal to classical prejudices. After all, counterintuitive assumptions—for example, that the speed of light is independent of an observer’s motion—have led to deep and valid consequences.The comment by Ruth Kastner states that phase randomness is key for decoherence and quantum Darwinism and that it is unlikely. Both are incorrect: Random phases between states are typical when phases can be defined. Moreover, random phases aren’t essential for decoherence; an outflow of information suffices. Indeed, standard models—for example, of quantum Brownian motion—often employ environments in equilibrium, for which phases are undefined and the question of their randomness is ill-posed. An initial correlation with the environment complicates calculations,22. L. D. Romero, J. P. Paz, Phys. Rev. A 55, 4070 (1997). https://doi.org/10.1103/PhysRevA.55.4070 but it does not eliminate decoherence. As difficulties encountered by quantum computing research show, decoherence is generic and hard to avoid.Quantum Darwinism requires more than decoherence; it relies on an environment that can store and communicate information. Solar radiation enables that,33. C. J. Riedel, W. H. Zurek, Phys. Rev. Lett. 105, 020404 (2010); https://doi.org/10.1103/PhysRevLett.105.020404New J. Phys. 13, 073038 (2011); https://doi.org/10.1088/1367-2630/13/7/073038M. Zwolak, C. J. Riedel, W. H. Zurek, Phys. Rev. Lett. 112, 140406 (2014). https://doi.org/10.1103/PhysRevLett.112.140406 since the Sun is a localized photon source. Quantum Darwinism is impossible in a completely equilibrated environment, whose subsystems cannot store information.The question of how to define systems is indeed of interest, and I have noted it before.44. W. H. Zurek, Phil. Trans. Roy. Soc. A 356, 1793 (1998); https://doi.org/10.1098/rsta.1998.0250Rev. Mod. Phys. 75, 715 (2003). https://doi.org/10.1103/RevModPhys.75.715 The answer must go beyond decoherence: What constitutes a system depends on interactions that make or break it; molecules, for example, would fall apart if atomic interactions weakened.There is no reason to complicate matters by making the definition of a system part of the measurement problem. Systems are there from the start—Schrödinger’s cat is obviously distinct from the nucleus that determines the cat’s fate—and their presence alone does not solve the problem. Indeed, the measurement problem disappears absent a system distinct from a measuring apparatus. Quantum evolution of a universe without parts is deterministic. There is no apparatus to record a definite outcome and so no need to talk about measurement outcomes: There is literally nothing to explain. Recognizing the role of the environment—as another system—is then natural in seeking answers.I am in good company when accused of the H-theorem “mistake.” Still, Ludwig Boltzmann dealt with the evolution of a many-body system that is classical and isolated. In that classical setting, probability was a fault of an observer ignorant of the system’s precise state. Boltzmann’s Stosszahlansatz postulates uncorrelated trajectories and is a way of representing that ignorance. Although the Boltzmann equation is useful, calling on Stosszahlansatz to prove the H-theorem—that is, the second law of thermodynamics—was suspect. Evolution is deterministic and reversible, so while observers’ ignorance may increase, microscopic entropy of the closed system cannot change. Moreover, the information and hence ignorance of observers is irrelevant for classical dynamics.As I show in my article, in our quantum world probabilities arise via entanglement. A single photon that escapes with information about the fate of Schrödinger’s cat is enough to decohere the cat’s state. An observer can never catch up with the photon, so reversibility of the equations of motion notwithstanding, information loss can be irreversible for prosaic yet compelling reasons. The resulting entropy production can be accounted for by decoherence.55. W. H. Zurek, J. P. Paz, Phys. Rev. Lett. 72, 2508 (1994). https://doi.org/10.1103/PhysRevLett.72.2508The whole measurement (or Schrödinger’s cat) setup starts far from equilibrium. Quantum Darwinism and decoherence show why, in such nonequilibrium multipartite settings, pointer states—and not their superpositions—survive and information about them is amplified and recorded in many copies by the environment. Both the nonequilibrium setting and the division of the universe into systems are needed to state the problem. When certain assumptions are needed to state the problem, surely they can be used to solve it.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. M. Zwolak, W. H. Zurek, Sci. Rep. 3, 1729 (2013); https://doi.org/10.1038/srep01729, Google ScholarCrossrefA. Streltsov, W. H. Zurek, Phys. Rev. Lett. 111, 040401 (2013). https://doi.org/10.1103/PhysRevLett.111.040401, , Google ScholarCrossref2. L. D. Romero, J. P. Paz, Phys. Rev. A 55, 4070 (1997). https://doi.org/10.1103/PhysRevA.55.4070, Google ScholarCrossref3. C. J. Riedel, W. H. Zurek, Phys. Rev. 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We determine the total state dynamics of a dephasing open quantum system using the standard environment of harmonic oscillators. Of particular interest are random unitary approaches to the same reduced dynamics and system-environment correlations in the full model. Concentrating on a model with an at times negative dephasing rate, the issue of non-Markovianity will also be addressed. Crucially, given the quantum environment, the appearance of non-Markovian dynamics turns out to be accompanied by a loss of system-environment correlations. Depending on the initial purity of the qubit state, these system-environment correlations may be purely classical over the whole relevant time scale, or there may be intervals of genuine system-environment entanglement. In the latter case, we see no obvious relation between the build-up or decay of these quantum correlations and Non-Markovianity.