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Physics Today

A last word on quantum Darwinism

Wojciech Hubert Zurek

Published Nov 30, 2015• 0 citations
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Abstract

Zurek replies: When quantum objects interact, they can entangle, as does a system with an apparatus or environment in models of measurement or of decoherence. The envariance-based derivation I gave of Born’s rule relies on a quantum indeterminacy that precludes simultaneous complete knowledge of both the entangled whole and its parts. Probabilities that quantify the resulting ignorance about parts follow from symmetries of entanglement.The so-called problem of outcomes is therefore not a bug but a feature of quantum physics: The ignorance it reflects leads to Born’s rule.Ignorance disappears only when an observer correlates with an outcome, precipitating a specific perception. Observers acquire information indirectly, using environments—photons, for example—as communication channels.Quantum Darwinism recognizes that decoherence doesn’t just hide quantum information. Rather, an environment is a repository and a conduit for multiple copies of information about outcomes, classical pointer states that survive decoherence intact. Flagrantly quantum effects are simultaneously hidden out of the observer’s reach.11. M. Zwolak, W. H. Zurek, Sci. Rep. 3, 1729 (2013). https://doi.org/10.1038/srep01729Classical physics dealt with an objective reality that was believed to exist and evolve independently of information. Measurements had predetermined outcomes. Information was an inconsequential illusion, irrelevant to what happened. In the classical universe, observers were like puppets, their strings pulled by Newtonian dynamics.Quantum theory shattered that view. Information is no longer a shadow of the classical states of a clockwork universe; it helps define the underlying quantum states. When a state is entangled, the ignorance of outcomes implied by quantum indeterminacy yields the probabilities that are reflected in the mixed state of the system.This interdependence between what is and what is known means that a quantum state represents partly existence and partly information. In the classical world, one could theorize about the precise state of the system and blame ignorance on observers. When, in our quantum universe, a pure entangled state is known, that fact implies complementary ignorance about parts; information and existence are inextricably intertwined.The decohered cat is neither dead nor alive. However, it is also no longer a superposition of dead and alive. The information amplified by decoherence and disseminated—for example, by photons—contains multiple records of the fate of the cat. Observers will agree about what happened and will take for granted the objective nature of the past.22. C. J. Riedel, W. H. Zurek, M. Zwolak, arXiv:1312.0331REFERENCESSection:ChooseTop of pageREFERENCES <<1. M. Zwolak, W. H. Zurek, Sci. Rep. 3, 1729 (2013). https://doi.org/10.1038/srep01729, Google ScholarCrossref2. C. J. Riedel, W. H. Zurek, M. Zwolak, arXiv:1312.0331, Google Scholar© 2015 American Institute of Physics.

DOI
10.1063/pt.3.3003

Related papers

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

A last word on quantum Darwinism

Art Hobson

In the opening paragraphs of “Quantum Darwinism, classical reality, and the randomness of quantum jumps” (Physics Today, October 2014, page 44), Wojciech Zurek invokes an analogue to Schrödinger’s cat and describes how the environment-driven process of decoherence removes the interferences that would otherwise exist between the live and dead states. He thus explains how the environment effectively “measures” the state of the cat. The article leaves me uncertain whether Zurek judges those comments to be a resolution of the quantum measurement or “Schrödinger’s cat” problem, but some readers might conclude that they indeed offer such a solution. Those readers would be wrong. As Stephen Adler has shown,11. S. L. Adler, Stud. Hist. Philos. Mod. Phys. 34, 135 (2003). https://doi.org/10.1016/S1355-2198(02)00086-2 and as decoherence expert Maximilian Schlosshauer has stated,22. M. Schlosshauer, Rev. Mod. Phys. 76, 1267 (2005). https://doi.org/10.1103/RevModPhys.76.1267 decoherence does not solve the measurement problem because it does not solve the so-called “problem of outcomes.”Decoherence theory shows how interactions with environmental quanta (photons, air molecules, and so forth) convert a quantum system’s superposition state α|s1⟩ + β|s2⟩ into the entangled “measurement state” α|s1⟩|e1⟩ + β|s2⟩|e2⟩, where |e1⟩ and |e2⟩ are orthogonal many-body states of the environment. Thus the environment acts just like a “which-slit” detector in the double-slit experiment with photons. Such a which-slit measurement transforms each photon from its premeasurement superposition over both slits into a measured photon whose single-slit states |s1⟩ and |s2⟩ are entangled with the two orthogonal states |e1⟩ and |e2⟩ of the detector. That removes the interferences from—that is, it decoheres—the photon.At that point, the theory runs into the problem of outcomes: The measurement state is still a superposition, albeit one in which the measured quantum no longer interferes with itself. By what logic does that imply definite (but indeterminate) individual outcomes? In other words, by what logic is Schrödinger’s cat converted into a cat that is either dead or alive rather than one that is both dead and alive? Zurek’s analysis does nothing to resolve that question.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. S. L. Adler, Stud. Hist. Philos. Mod. Phys. 34, 135 (2003). https://doi.org/10.1016/S1355-2198(02)00086-2, Google ScholarCrossref2. M. Schlosshauer, Rev. Mod. Phys. 76, 1267 (2005). https://doi.org/10.1103/RevModPhys.76.1267, Google ScholarCrossref© 2015 American Institute of Physics.

Physics Today•Nov 30, 2015•1 citation

Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons

Wojciech Hubert Zurek

Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that—when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate)—these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate. This approach shares with the Relative State Interpretation of Everett the view that collapse of the wavepacket reflects perception of the state of the rest of the Universe relative to the state of observer’s records. However, our “let quantum be quantum” approach poses questions absent in Bohr’s Copenhagen Interpretation that relied on the preexisting classical domain. Thus, one is now forced to seek preferred, predictable, hence effectively classical but ultimately quantum states that allow observers keep reliable records. Without such (i) preferred basis relative states are simply “too relative”, and the ensuing basis ambiguity makes it difficult to identify events (e.g., measurement outcomes). Moreover, universal validity of quantum theory raises the issue of (ii) the origin of Born’s rule, pk=|ψk|2, relating probabilities and amplitudes (that is simply postulated in textbooks). Last not least, even preferred pointer states (defined by einselection—environment—induced superselection)—are still quantum. Therefore, unlike classical states that exist objectively, quantum states of an individual system cannot be found out by an initially ignorant observer through direct measurement without being disrupted. So, to complete the ‘quantum theory of the classical’ one must identify (iii) quantum origin of objective existence and explain how the information about objectively existing states can appear to be essentially inconsequential for them (as it does for states in Newtonian physics) and yet matter in other settings (e.g., thermodynamics). I show how the mathematical structure of quantum theory supplemented by the only uncontroversial measurement postulate (that demands immediate repeatability—hence, predictability) leads to preferred states. These (i) pointer states correspond to measurement outcomes. Their stability is a prerequisite for objective existence of effectively classical states and for events such as quantum jumps. Events at hand, one can now enquire about their probability—the probability of a pointer state (or of a measurement record). I show that the symmetry of entangled states—(ii) entanglement—assisted invariance or envariance—implies Born’s rule. Envariance also accounts for the loss of phase coherence between pointer states. Thus, decoherence can be traced to symmetries of entanglement and understood without its usual tool—reduced density matrices. A simple and manifestly noncircular derivation of pk=|ψk|2 follows. Monitoring of the system by its environment in course of decoherence typically leaves behind multiple copies of its pointer states in the environment. Only pointer states can survive decoherence and can spawn such plentiful information-theoretic progeny. This (iii) quantum Darwinism allows observers to use environment as a witness—to find out pointer states indirectly, leaving systems of interest untouched. Quantum Darwinism shows how epistemic and ontic (coexisting in epiontic quantum state) separate into robust objective existence of pointer states and detached information about them, giving rise to extantons—composite objects with system of interest in the core and multiple records of its pointer states in the halo comprising of environment subsystems (e.g., photons) which disseminates that information throughout the Universe.

arXiv:2208.09019•Entropy•Oct 24, 2022•56 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

Quantum theory of the classical: quantum jumps, Born’s Rule and objective classical reality via quantum Darwinism

Wojciech Hubert Zurek

The emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. In this paper, I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with the derivation of preferred sets of states that help to define what exists—our everyday classical reality. They emerge as a result of the breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification—of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and the emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection . The pointer states obtained in this way determine what can happen—define events—without appealing to Born’s Rule for probabilities. Therefore, p k =| ψ k | 2 can now be deduced from the entanglement-assisted invariance, or envariance —a symmetry of entangled quantum states. With probabilities at hand, one also gains new insights into the foundations of quantum statistical physics. Moreover, one can now analyse the information flows responsible for decoherence. These information flows explain how the perception of objective classical reality arises from the quantum substrate: the effective amplification that they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment—through quantum Darwinism . This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

arXiv:1807.02092•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•May 28, 2018•49 citations

Born’s Rule from the Symmetries of Entanglement

Wojciech Hubert Zurek

Chapter 3 describes how quantum entanglement leads to probabilities based on a symmetry, but—in contrast to subjective equal likelihood based solely on ignorance—it is an objective symmetry of known quantum states. Entanglement-assisted invariance (or envariance for short) relies on quantum correlations: One can know the quantum state of the whole and use this to quantify the resulting ignorance of the states of parts. Thus, quantum probability is, in effect, an objective consequence of the Heisenberg-like indeterminacy between global and local observables. This derivation of Born’s rule is based on the consistent subset of quantum postulates. It justifies statistical interpretation of reduced density matrices, an indispensable tool of decoherence theory. Hence, it gives one the mandate to explore—in Part II of this book—the fundamental implications of decoherence and its consequences using reduced density matrices and other customary tools.

Cambridge University Press eBooks•Mar 6, 2025•0 citations
Zurek replies: When quantum objects interact, they can entangle, as does a system with an apparatus or environment in models of measurement or of decoherence. The envariance-based derivation I gave of Born’s rule relies on a quantum indeterminacy that precludes simultaneous complete knowledge of both the entangled whole and its parts. Probabilities that quantify the resulting ignorance about parts follow from symmetries of entanglement.The so-called problem of outcomes is therefore not a bug but a feature of quantum physics: The ignorance it reflects leads to Born’s rule.Ignorance disappears only when an observer correlates with an outcome, precipitating a specific perception. Observers acquire information indirectly, using environments—photons, for example—as communication channels.Quantum Darwinism recognizes that decoherence doesn’t just hide quantum information. Rather, an environment is a repository and a conduit for multiple copies of information about outcomes, classical pointer states that survive decoherence intact. Flagrantly quantum effects are simultaneously hidden out of the observer’s reach.11. M. Zwolak, W. H. Zurek, Sci. Rep. 3, 1729 (2013). https://doi.org/10.1038/srep01729Classical physics dealt with an objective reality that was believed to exist and evolve independently of information. Measurements had predetermined outcomes. Information was an inconsequential illusion, irrelevant to what happened. In the classical universe, observers were like puppets, their strings pulled by Newtonian dynamics.Quantum theory shattered that view. Information is no longer a shadow of the classical states of a clockwork universe; it helps define the underlying quantum states. When a state is entangled, the ignorance of outcomes implied by quantum indeterminacy yields the probabilities that are reflected in the mixed state of the system.This interdependence between what is and what is known means that a quantum state represents partly existence and partly information. In the classical world, one could theorize about the precise state of the system and blame ignorance on observers. When, in our quantum universe, a pure entangled state is known, that fact implies complementary ignorance about parts; information and existence are inextricably intertwined.The decohered cat is neither dead nor alive. However, it is also no longer a superposition of dead and alive. The information amplified by decoherence and disseminated—for example, by photons—contains multiple records of the fate of the cat. Observers will agree about what happened and will take for granted the objective nature of the past.22. C. J. Riedel, W. H. Zurek, M. Zwolak, arXiv:1312.0331REFERENCESSection:ChooseTop of pageREFERENCES <<1. M. Zwolak, W. H. Zurek, Sci. Rep. 3, 1729 (2013). https://doi.org/10.1038/srep01729, Google ScholarCrossref2. C. J. Riedel, W. H. Zurek, M. Zwolak, arXiv:1312.0331, Google Scholar© 2015 American Institute of Physics.
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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In the opening paragraphs of “Quantum Darwinism, classical reality, and the randomness of quantum jumps” (Physics Today, October 2014, page 44), Wojciech Zurek invokes an analogue to Schrödinger’s cat and describes how the environment-driven process of decoherence removes the interferences that would otherwise exist between the live and dead states. He thus explains how the environment effectively “measures” the state of the cat. The article leaves me uncertain whether Zurek judges those comments to be a resolution of the quantum measurement or “Schrödinger’s cat” problem, but some readers might conclude that they indeed offer such a solution. Those readers would be wrong. As Stephen Adler has shown,11. S. L. Adler, Stud. Hist. Philos. Mod. Phys. 34, 135 (2003). https://doi.org/10.1016/S1355-2198(02)00086-2 and as decoherence expert Maximilian Schlosshauer has stated,22. M. Schlosshauer, Rev. Mod. Phys. 76, 1267 (2005). https://doi.org/10.1103/RevModPhys.76.1267 decoherence does not solve the measurement problem because it does not solve the so-called “problem of outcomes.”Decoherence theory shows how interactions with environmental quanta (photons, air molecules, and so forth) convert a quantum system’s superposition state α|s1⟩ + β|s2⟩ into the entangled “measurement state” α|s1⟩|e1⟩ + β|s2⟩|e2⟩, where |e1⟩ and |e2⟩ are orthogonal many-body states of the environment. Thus the environment acts just like a “which-slit” detector in the double-slit experiment with photons. Such a which-slit measurement transforms each photon from its premeasurement superposition over both slits into a measured photon whose single-slit states |s1⟩ and |s2⟩ are entangled with the two orthogonal states |e1⟩ and |e2⟩ of the detector. That removes the interferences from—that is, it decoheres—the photon.At that point, the theory runs into the problem of outcomes: The measurement state is still a superposition, albeit one in which the measured quantum no longer interferes with itself. By what logic does that imply definite (but indeterminate) individual outcomes? In other words, by what logic is Schrödinger’s cat converted into a cat that is either dead or alive rather than one that is both dead and alive? Zurek’s analysis does nothing to resolve that question.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. S. L. Adler, Stud. Hist. Philos. Mod. Phys. 34, 135 (2003). https://doi.org/10.1016/S1355-2198(02)00086-2, Google ScholarCrossref2. M. Schlosshauer, Rev. Mod. Phys. 76, 1267 (2005). https://doi.org/10.1103/RevModPhys.76.1267, Google ScholarCrossref© 2015 American Institute of Physics.
Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that—when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate)—these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate. This approach shares with the Relative State Interpretation of Everett the view that collapse of the wavepacket reflects perception of the state of the rest of the Universe relative to the state of observer’s records. However, our “let quantum be quantum” approach poses questions absent in Bohr’s Copenhagen Interpretation that relied on the preexisting classical domain. Thus, one is now forced to seek preferred, predictable, hence effectively classical but ultimately quantum states that allow observers keep reliable records. Without such (i) preferred basis relative states are simply “too relative”, and the ensuing basis ambiguity makes it difficult to identify events (e.g., measurement outcomes). Moreover, universal validity of quantum theory raises the issue of (ii) the origin of Born’s rule, pk=|ψk|2, relating probabilities and amplitudes (that is simply postulated in textbooks). Last not least, even preferred pointer states (defined by einselection—environment—induced superselection)—are still quantum. Therefore, unlike classical states that exist objectively, quantum states of an individual system cannot be found out by an initially ignorant observer through direct measurement without being disrupted. So, to complete the ‘quantum theory of the classical’ one must identify (iii) quantum origin of objective existence and explain how the information about objectively existing states can appear to be essentially inconsequential for them (as it does for states in Newtonian physics) and yet matter in other settings (e.g., thermodynamics). I show how the mathematical structure of quantum theory supplemented by the only uncontroversial measurement postulate (that demands immediate repeatability—hence, predictability) leads to preferred states. These (i) pointer states correspond to measurement outcomes. Their stability is a prerequisite for objective existence of effectively classical states and for events such as quantum jumps. Events at hand, one can now enquire about their probability—the probability of a pointer state (or of a measurement record). I show that the symmetry of entangled states—(ii) entanglement—assisted invariance or envariance—implies Born’s rule. Envariance also accounts for the loss of phase coherence between pointer states. Thus, decoherence can be traced to symmetries of entanglement and understood without its usual tool—reduced density matrices. A simple and manifestly noncircular derivation of pk=|ψk|2 follows. Monitoring of the system by its environment in course of decoherence typically leaves behind multiple copies of its pointer states in the environment. Only pointer states can survive decoherence and can spawn such plentiful information-theoretic progeny. This (iii) quantum Darwinism allows observers to use environment as a witness—to find out pointer states indirectly, leaving systems of interest untouched. Quantum Darwinism shows how epistemic and ontic (coexisting in epiontic quantum state) separate into robust objective existence of pointer states and detached information about them, giving rise to extantons—composite objects with system of interest in the core and multiple records of its pointer states in the halo comprising of environment subsystems (e.g., photons) which disseminates that information throughout the Universe.
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 emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. In this paper, I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with the derivation of preferred sets of states that help to define what exists—our everyday classical reality. They emerge as a result of the breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification—of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and the emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection . The pointer states obtained in this way determine what can happen—define events—without appealing to Born’s Rule for probabilities. Therefore, p k =| ψ k | 2 can now be deduced from the entanglement-assisted invariance, or envariance —a symmetry of entangled quantum states. With probabilities at hand, one also gains new insights into the foundations of quantum statistical physics. Moreover, one can now analyse the information flows responsible for decoherence. These information flows explain how the perception of objective classical reality arises from the quantum substrate: the effective amplification that they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment—through quantum Darwinism . This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.
Chapter 3 describes how quantum entanglement leads to probabilities based on a symmetry, but—in contrast to subjective equal likelihood based solely on ignorance—it is an objective symmetry of known quantum states. Entanglement-assisted invariance (or envariance for short) relies on quantum correlations: One can know the quantum state of the whole and use this to quantify the resulting ignorance of the states of parts. Thus, quantum probability is, in effect, an objective consequence of the Heisenberg-like indeterminacy between global and local observables. This derivation of Born’s rule is based on the consistent subset of quantum postulates. It justifies statistical interpretation of reduced density matrices, an indispensable tool of decoherence theory. Hence, it gives one the mandate to explore—in Part II of this book—the fundamental implications of decoherence and its consequences using reduced density matrices and other customary tools.