Special Issue "Quantum Darwinism and Friends"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (15 December 2021) | Viewed by 17283

Special Issue Editors

Dr. Sebastian Deffner
E-Mail Website
Guest Editor
Department of Physics, UMBC, Baltimore, MD 21250, USA
Interests: quantum thermodynamics; theoretical physics; statistical physics; quantum control; quantum speed limit; shortcuts to adiabaticity; quantum information theory; foundations of physics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Raymond Laflamme
E-Mail Website
Guest Editor
Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Interests: quantum information; robust quantum control; experimental quantum information processing; quantum cryptography
Prof. Dr. Juan Pablo Paz
E-Mail Website
Guest Editor
Departamento de Física, FCEyN, UBA, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Interests: quantum foundations; quantum information; quantum thermodynamics; quantum optics
Dr. Michael Zwolak
E-Mail Website
Guest Editor
Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
Interests: quantum foundations; catalytic processes at the nanoscale; nanofluidic devices; measurement techniques

Special Issue Information

Wojciech Hubert Zurek has made seminal contributions to several areas of theoretical physics. This includes decoherence, where he had the key insight that physical environments superselect certain “pointer” states, and the foundations of quantum and classical information (e.g., the no-cloning theorem and quantum discord). His work on the dynamics of non-equilibrium phase transitions led to the Kibble–Zurek mechanism. Quantum Darwinism—the subject of this volume—is a culmination of advances that started with decoherence. It accounts for the emergence of objective classical reality in our quantum universe.
 
Wojciech Zurek earned his MSc in Krakow, in his native Poland, and his PhD at the University of Texas at Austin, where he remained until 1981 as a postdoctoral fellow of John Archibald Wheeler. In 1981, Zurek joined the group of Kip Thorne at Caltech as a Tolman Fellow and arrived at Los Alamos in 1984 as an Oppenheimer Fellow. He rose to the position of group leader of the Theoretical Astrophysics Group in 1991. In 1996, Zurek was named Laboratory Fellow of the Theory Division. 

In his long career, Wojciech Zurek has won many honors and awards. A non-comprehensive list includes the Phi Beta Kappa Visiting Lecturer (2004), the Alexander von Humboldt Prize (2005), the Marian Smoluchowski Medal (2009), the Albert Einstein Professorship (awarded in 2010 by the Ulm University), the Order of Polonia Restituta (2012), and the Los Alamos Medal (2014).

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How many of us have heard, or maybe even made, the statement that “quantum mechanics is weird”? As human beings that evolved at classical energy and lengths scales, we are so used to the fact that things look “classical” that the actual workings of our quantum Universe constantly have us in awe, confuse us, and sometimes even appall us.

Take, for instance, the frequently maltreated cat. If any two of us look at the same cat, we will both conclude that we are looking at a cat. Well, actually, we conclude that we both “perceive” a cat, and we will agree about its state of well-being. From a fundamental point of view, the question has to be: why? The answer originates in the fact that any fraction of photons that we intercept with our eyes carries the same, classical information about the lovely beast. The more formal analysis of the emergence of this classical objectivity is known as Quantum Darwinism, as it relies on Darwinian fitness of certain states—their ability to not just survive immersion in the environment, but create, multiple “offspring” of the information about themselves in the photon (and other) environments, where they can be accessed by observers such as us.

Quantum Darwinism shows how the perception of objective classical reality arises via selective amplification and the spreading of information in our fundamentally quantum universe. Quantum Darwinism goes beyond decoherence, as it recognizes that the many copies of the system’s pointer states are imprinted on the environment: agents acquire data indirectly, by intercepting environment fragments (rather than directly measuring systems of interest). The data disseminated through the environment provide us with shared information about stable, effectively classical pointer states. Humans rely primarily on the photon environment, eavesdropping on “objects of interest” by intercepting tiny fractions of photons that contributed to decoherence.

In honor of Wojciech Zurek’s 70th birthday, this Special Issue is dedicated to recent advances in the field and pays tribute to Zurek’s seminal contributions to our understanding of the Universe. To this end, “Quantum Darwinism and Friends” collects articles that make sense of the apparent chasm between quantum weirdness and classical perception, and provides a snapshot of this fundamental, exciting, and vivid field of theoretical physics.

Dr. Sebastian Deffner
Prof. Dr. Raymond Laflamme
Prof. Dr. Juan Pablo Paz
Dr. Michael Zwolak
Guest Editors

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Published Papers (17 papers)

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Research

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Article
Amplification, Inference, and the Manifestation of Objective Classical Information
Entropy 2022, 24(6), 781; https://doi.org/10.3390/e24060781 - 01 Jun 2022
Cited by 2 | Viewed by 686
Abstract
Our everyday reality is characterized by objective information—information that is selected and amplified by the environment that interacts with quantum systems. Many observers can accurately infer that information indirectly by making measurements on fragments of the environment. The correlations between the system, S [...] Read more.
Our everyday reality is characterized by objective information—information that is selected and amplified by the environment that interacts with quantum systems. Many observers can accurately infer that information indirectly by making measurements on fragments of the environment. The correlations between the system, S, and a fragment, F, of the environment, E, is often quantified by the quantum mutual information, or the Holevo quantity, which bounds the classical information about S transmittable by a quantum channel F. The latter is a quantum mutual information but of a classical-quantum state where measurement has selected outcomes on S. The measurement generically reflects the influence of the remaining environment, E/F, but can also reflect hypothetical questions to deduce the structure of SF correlations. Recently, Touil et al. examined a different Holevo quantity, one from a quantum-classical state (a quantum S to a measured F). As shown here, this quantity upper bounds any accessible classical information about S in F and can yield a tighter bound than the typical Holevo quantity. When good decoherence is present—when the remaining environment, E/F, has effectively measured the pointer states of S—this accessibility bound is the accessible information. For the specific model of Touil et al., the accessible information is related to the error probability for optimal detection and, thus, has the same behavior as the quantum Chernoff bound. The latter reflects amplification and provides a universal approach, as well as a single-shot framework, to quantify records of the missing, classical information about S. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Article
Quantum Coherences and Classical Inhomogeneities as Equivalent Thermodynamics Resources
Entropy 2022, 24(4), 474; https://doi.org/10.3390/e24040474 - 29 Mar 2022
Cited by 2 | Viewed by 830
Abstract
Quantum energy coherences represent a thermodynamic resource, which can be exploited to extract energy from a thermal reservoir and deliver that energy as work. We argue that there exists a closely analogous classical thermodynamic resource, namely, energy-shell inhomogeneities in the phase space distribution [...] Read more.
Quantum energy coherences represent a thermodynamic resource, which can be exploited to extract energy from a thermal reservoir and deliver that energy as work. We argue that there exists a closely analogous classical thermodynamic resource, namely, energy-shell inhomogeneities in the phase space distribution of a system’s initial state. We compare the amount of work that can be obtained from quantum coherences with the amount that can be obtained from classical inhomogeneities, and find them to be equal in the semiclassical limit. We thus conclude that coherences do not provide a unique thermodynamic advantage of quantum systems over classical systems, in situations where a well-defined semiclassical correspondence exists. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Article
Non-Perfect Propagation of Information to a Noisy Environment with Self-Evolution
Entropy 2022, 24(4), 467; https://doi.org/10.3390/e24040467 - 28 Mar 2022
Viewed by 599
Abstract
We study the non-perfect propagation of information for evolving a low-dimensional environment that includes self-evolution as well as noisy initial states and analyse the interrelations between the degree of objectivization and environment parameters. In particular, we consider an analytical model of three interacting [...] Read more.
We study the non-perfect propagation of information for evolving a low-dimensional environment that includes self-evolution as well as noisy initial states and analyse the interrelations between the degree of objectivization and environment parameters. In particular, we consider an analytical model of three interacting qubits and derive its objectivity parameters. The numerical analysis shows that the quality of the spectrum broadcast structure formed during the interaction may exhibit non-monotonicity both in the speed of self-dynamics of the environment as well as its mixedness. The former effect is particularly strong, showing that—considering part of the environment as a measurement apparatus—an increase of the external magnetic field acting on the environment may turn the vague measurement into close to ideal. The above effects suggest that quantum objectivity may appear after increasing the dynamics of the environment, although not with respect to the pointer basis, but some other, which we call the generalized pointer or indicator basis. Furthermore, it seems also that, when the objectivity is poor, it may be improved, at least by some amount, by increasing the thermal noise. We provide further evidence of this by analysing the upper bounds on distance to the set of states representing perfect objectivity in the case of a higher number of qubits. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Article
Equilibration and “Thermalization” in the Adapted Caldeira–Leggett Model
Entropy 2022, 24(3), 316; https://doi.org/10.3390/e24030316 - 23 Feb 2022
Cited by 1 | Viewed by 569
Abstract
I explore the processes of equilibration exhibited by the Adapted Caldeira–Leggett (ACL) model, a small unitary “toy model” developed for numerical studies of quantum decoherence between an SHO and an environment. I demonstrate how dephasing allows equilibration to occur in a wide variety [...] Read more.
I explore the processes of equilibration exhibited by the Adapted Caldeira–Leggett (ACL) model, a small unitary “toy model” developed for numerical studies of quantum decoherence between an SHO and an environment. I demonstrate how dephasing allows equilibration to occur in a wide variety of situations. While the finite model size and other “unphysical” aspects prevent the notions of temperature and thermalization from being generally applicable, certain primitive aspects of thermalization can be realized for particular parameter values. I link the observed behaviors to intrinsic properties of the global energy eigenstates, and argue that the phenomena I observe contain elements which might be key ingredients that lead to ergodic behavior in larger more realistic systems. The motivations for this work range from curiosity about phenomena observed in earlier calculations with the ACL model to much larger questions related to the nature of equilibrium, thermalization, and the emergence of physical laws. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Article
Emergence of Objectivity for Quantum Many-Body Systems
Entropy 2022, 24(2), 277; https://doi.org/10.3390/e24020277 - 14 Feb 2022
Cited by 1 | Viewed by 868
Abstract
We examine the emergence of objectivity for quantum many-body systems in a setting without an environment to decohere the system’s state, but where observers can only access small fragments of the whole system. We extend the result of Reidel (2017) to the case [...] Read more.
We examine the emergence of objectivity for quantum many-body systems in a setting without an environment to decohere the system’s state, but where observers can only access small fragments of the whole system. We extend the result of Reidel (2017) to the case where the system is in a mixed state, measurements are performed through POVMs, and imprints of the outcomes are imperfect. We introduce a new condition on states and measurements to recover full classicality for any number of observers. We further show that evolutions of quantum many-body systems can be expected to yield states that satisfy this condition whenever the corresponding measurement outcomes are redundant. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
Article
Revisiting Born’s Rule through Uhlhorn’s and Gleason’s Theorems
Entropy 2022, 24(2), 199; https://doi.org/10.3390/e24020199 - 28 Jan 2022
Cited by 2 | Viewed by 829
Abstract
In a previous article we presented an argument to obtain (or rather infer) Born’s rule, based on a simple set of axioms named “Contexts, Systems and Modalities" (CSM). In this approach, there is no “emergence”, but the structure of quantum mechanics can be [...] Read more.
In a previous article we presented an argument to obtain (or rather infer) Born’s rule, based on a simple set of axioms named “Contexts, Systems and Modalities" (CSM). In this approach, there is no “emergence”, but the structure of quantum mechanics can be attributed to an interplay between the quantized number of modalities that is accessible to a quantum system and the continuum of contexts that are required to define these modalities. The strong link of this derivation with Gleason’s theorem was emphasized, with the argument that CSM provides a physical justification for Gleason’s hypotheses. Here, we extend this result by showing that an essential one among these hypotheses—the need of unitary transforms to relate different contexts—can be removed and is better seen as a necessary consequence of Uhlhorn’s theorem. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
Article
A Classical Formulation of Quantum Theory?
Entropy 2022, 24(1), 137; https://doi.org/10.3390/e24010137 - 17 Jan 2022
Cited by 1 | Viewed by 733
Abstract
We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start with is epistemically restricted, in the spirit of a model [...] Read more.
We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start with is epistemically restricted, in the spirit of a model introduced by Spekkens. We obtain quantum theory only by combining a collection of restricted classical pictures. Our main challenge in this paper is to find a simple way of characterizing the allowed sets of classical pictures. We present one promising approach to this problem and show how it works out for the case of a single qubit. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
Article
Does Decoherence Select the Pointer Basis of a Quantum Meter?
Entropy 2022, 24(1), 106; https://doi.org/10.3390/e24010106 - 10 Jan 2022
Viewed by 511
Abstract
The consensus regarding quantum measurements rests on two statements: (i) von Neumann’s standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the “meter”) unambiguously determines the measuring (“pointer”) basis. The [...] Read more.
The consensus regarding quantum measurements rests on two statements: (i) von Neumann’s standard quantum measurement theory leaves undetermined the basis in which observables are measured, and (ii) the environmental decoherence of the measuring device (the “meter”) unambiguously determines the measuring (“pointer”) basis. The latter statement means that the environment monitors (measures) selected observables of the meter and (indirectly) of the system. Equivalently, a measured quantum state must end up in one of the “pointer states” that persist in the presence of the environment. We find that, unless we restrict ourselves to projective measurements, decoherence does not necessarily determine the pointer basis of the meter. Namely, generalized measurements commonly allow the observer to choose from a multitude of alternative pointer bases that provide the same information on the observables, regardless of decoherence. By contrast, the measured observable does not depend on the pointer basis, whether in the presence or in the absence of decoherence. These results grant further support to our notion of Quantum Lamarckism, whereby the observer’s choices play an indispensable role in quantum mechanics. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
Article
Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion
Entropy 2021, 23(12), 1602; https://doi.org/10.3390/e23121602 - 29 Nov 2021
Cited by 2 | Viewed by 752
Abstract
Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of [...] Read more.
Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum–classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Article
Quantifying Decoherence via Increases in Classicality
Entropy 2021, 23(12), 1594; https://doi.org/10.3390/e23121594 - 28 Nov 2021
Viewed by 622
Abstract
As a direct consequence of the interplay between the superposition principle of quantum mechanics and the dynamics of open systems, decoherence is a recurring theme in both foundational and experimental exploration of the quantum realm. Decoherence is intimately related to information leakage of [...] Read more.
As a direct consequence of the interplay between the superposition principle of quantum mechanics and the dynamics of open systems, decoherence is a recurring theme in both foundational and experimental exploration of the quantum realm. Decoherence is intimately related to information leakage of open systems and is usually formulated in the setup of “system + environment” as information acquisition of the environment (observer) from the system. As such, it has been mainly characterized via correlations (e.g., quantum mutual information, discord, and entanglement). Decoherence combined with redundant proliferation of the system information to multiple fragments of environment yields the scenario of quantum Darwinism, which is now a widely recognized framework for addressing the quantum-to-classical transition: the emergence of the apparent classical reality from the enigmatic quantum substrate. Despite the half-century development of the notion of decoherence, there are still many aspects awaiting investigations. In this work, we introduce two quantifiers of classicality via the Jordan product and uncertainty, respectively, and then employ them to quantify decoherence from an information-theoretic perspective. As a comparison, we also study the influence of the system on the environment. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Article
Limits to Perception by Quantum Monitoring with Finite Efficiency
Entropy 2021, 23(11), 1527; https://doi.org/10.3390/e23111527 - 17 Nov 2021
Cited by 2 | Viewed by 796
Abstract
We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and [...] Read more.
We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent’s perception of the system is altered by access to additional information. We apply our results to Gaussian states and to the dynamics of a system embedded in an environment illustrated on a quantum Ising chain. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Article
Thermality versus Objectivity: Can They Peacefully Coexist?
Entropy 2021, 23(11), 1506; https://doi.org/10.3390/e23111506 - 13 Nov 2021
Cited by 5 | Viewed by 975
Abstract
Under the influence of external environments, quantum systems can undergo various different processes, including decoherence and equilibration. We observe that macroscopic objects are both objective and thermal, thus leading to the expectation that both objectivity and thermalisation can peacefully coexist on the quantum [...] Read more.
Under the influence of external environments, quantum systems can undergo various different processes, including decoherence and equilibration. We observe that macroscopic objects are both objective and thermal, thus leading to the expectation that both objectivity and thermalisation can peacefully coexist on the quantum regime too. Crucially, however, objectivity relies on distributed classical information that could conflict with thermalisation. Here, we examine the overlap between thermal and objective states. We find that in general, one cannot exist when the other is present. However, there are certain regimes where thermality and objectivity are more likely to coexist: in the high temperature limit, at the non-degenerate low temperature limit, and when the environment is large. This is consistent with our experiences that everyday-sized objects can be both thermal and objective. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Article
Environment-Assisted Shortcuts to Adiabaticity
Entropy 2021, 23(11), 1479; https://doi.org/10.3390/e23111479 - 09 Nov 2021
Cited by 2 | Viewed by 1221
Abstract
Envariance is a symmetry exhibited by correlated quantum systems. Inspired by this “quantum fact of life,” we propose a novel method for shortcuts to adiabaticity, which enables the system to evolve through the adiabatic manifold at all times, solely by controlling the environment. [...] Read more.
Envariance is a symmetry exhibited by correlated quantum systems. Inspired by this “quantum fact of life,” we propose a novel method for shortcuts to adiabaticity, which enables the system to evolve through the adiabatic manifold at all times, solely by controlling the environment. As the main results, we construct the unique form of the driving on the environment that enables such dynamics, for a family of composite states of arbitrary dimension. We compare the cost of this environment-assisted technique with that of counterdiabatic driving, and we illustrate our results for a two-qubit model. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Article
Many-Body Localization and the Emergence of Quantum Darwinism
Entropy 2021, 23(11), 1377; https://doi.org/10.3390/e23111377 - 20 Oct 2021
Cited by 4 | Viewed by 888
Abstract
Quantum Darwinism (QD) is the process responsible for the proliferation of redundant information in the environment of a quantum system that is being decohered. This enables independent observers to access separate environmental fragments and reach consensus about the system’s state. In this work, [...] Read more.
Quantum Darwinism (QD) is the process responsible for the proliferation of redundant information in the environment of a quantum system that is being decohered. This enables independent observers to access separate environmental fragments and reach consensus about the system’s state. In this work, we study the effect of disorder in the emergence of QD and find that a highly disordered environment is greatly beneficial for it. By introducing the notion of lack of redundancy to quantify objectivity, we show that it behaves analogously to the entanglement entropy (EE) of the environmental eigenstate taken as an initial state. This allows us to estimate the many-body mobility edge by means of our Darwinistic measure, implicating the existence of a critical degree of disorder beyond which the degree of objectivity rises the larger the environment is. The latter hints the key role that disorder may play when the environment is of a thermodynamic size. At last, we show that a highly disordered evolution may reduce the spoiling of redundancy in the presence of intra-environment interactions. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Article
Justifying Born’s Rule Pα = |Ψα|2 Using Deterministic Chaos, Decoherence, and the de Broglie–Bohm Quantum Theory
Entropy 2021, 23(11), 1371; https://doi.org/10.3390/e23111371 - 20 Oct 2021
Cited by 3 | Viewed by 746
Abstract
In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads [...] Read more.
In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution ρ(x) of finding a particle at point x to the Born probability law |Ψ(x)|2. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Article
Quantum Darwinism in a Composite System: Objectivity versus Classicality
Entropy 2021, 23(8), 995; https://doi.org/10.3390/e23080995 - 31 Jul 2021
Cited by 13 | Viewed by 1525
Abstract
We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an N-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an [...] Read more.
We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an N-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an analytical expression for the dynamics is obtained. It demonstrates that part of the system Hilbert space redundantly proliferates its information to the environment, while the remaining subspace is decoupled and preserves clear non-classical signatures. For measurements performed on the system, we establish that a non-zero quantum discord is shared between the composite system and the environment, thus violating the conditions of strong Darwinism. However, due to the asymmetry of quantum discord, the information shared with the environment is completely classical for measurements performed on the environment. Our results imply a dichotomy between objectivity and classicality that emerges when considering composite systems. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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Review

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Review
Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
Entropy 2022, 24(11), 1520; https://doi.org/10.3390/e24111520 - 24 Oct 2022
Cited by 1 | Viewed by 579
Abstract
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 [...] Read more.
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 einselectionenvironment—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. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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