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Register a new userUniqueness of the Observable Leaving Redundant Imprints in the Environment in the Context of Quantum Darwinism
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Hui-Feng Fu
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In quantum Darwinism, the pointer observable of a system leaves redundant imprints in its environment after decoherence. Each imprint is recorded in a fraction of the environment, which identifies a particular partition of the environment. An ambiguity situation may occur when another observable noncommuting to the pointer observable also leaves redundant imprints with respect to another partition of the environment. We study this problem based on a uniqueness theorem we proved. We find that within a particular subset of all possible partitions of the environment, the observable of the system leaving redundant and nondegenerately recorded imprints in the environment is unique. And, in a typical situation, the partitions outside this particular subset have no physical significance.
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Quantum Darwinism extends the traditional formalism of decoherence to explain the emergence of classicality in a quantum universe. A classical description emerges when the environment tends to redundantly acquire information about the pointer states of an open system. In light of recent interest, we apply the theoretical tools of the framework to a qubit coupled with many bosonic sub-environments. We examine the degree to which the same classical information is encoded across collections of: (i) complete sub-environments, and (ii) residual pseudomode components of each sub-environment, the conception of which provides a dynamic representation of the reservoir memory. Overall, significant redundancy of information is found as a typical result of the decoherence process. However, by examining its decomposition in terms of classical and quantum correlations, we discover classical information to be non-redundant in both cases (i) and (ii). Moreover, with the full collection of pseudomodes, certain dynamical regimes realize opposite effects, where either the total classical or quantum correlations predominantly decay over time. Finally, when the dynamics are non-Markovian, we find that redundant information is suppressed in line with information back-flow to the qubit. By quantifying redundancy, we concretely show it to act as a witness to non-Markovianity in the same way as the trace distance does for nondivisible dynamical maps.
We examine the emergence of objectivity via quantum Darwinism through the use of a collision model, i.e. where the dynamics is modeled through sequences of unitary interactions between the system and the individual constituents of the environment, termed ancillas. By exploiting versatility of this framework, we show that one can transition from a Darwinistic to an encoding environment by simply tuning their interaction. Furthermore we establish that in order for a setting to exhibit quantum Darwinism we require a mutual decoherence to occur between the system and environmental ancillas, thus showing that system decoherence alone is not sufficient. Finally, we demonstrate that the observation of quantum Darwinism is sensitive to a non-uniform system-environment interaction.
Quantum Darwinism proposes that the proliferation of redundant information plays a major role in the emergence of objectivity out of the quantum world. Is this kind of objectivity necessarily classical? We show that if one takes Spekkens notion of noncontextuality as the notion of classicality and the approach of Brand~{a}o, Piani and Horodecki to quantum Darwinism, the answer to the above question is `yes, if the environment encodes sufficiently well the proliferated information. Moreover, we propose a threshold on this encoding, above which one can unambiguously say that classical objectivity has emerged under quantum Darwinism.
Effective classicality of a property of a quantum system can be defined using redundancy of its record in the environment. This allows quantum physics to approximate the situation encountered in the classical world: The information about a classical system can exist independently from its state. In quantum theory this is no longer possible: In an isolated quantum system the state and the information about it are inextricably linked, and any measurement may -- and usually will -- reset that state. However, when the information about the state of a quantum system is spread throughout the environment, it can be treated (almost) as in classical physics.
We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles of states for a model universe consisting of one system and many environments: the first consisting of arbitrary states, and the second consisting of ``singly-branching states consistent with a simple decoherence model. Typical states from the random ensemble do not store information about the system redundantly, but information stored in branching states has a redundancy proportional to the environments size. We compute the specific redundancy for a wide range of model universes, and fit the results to a simple first-principles theory. Our results show that the presence of redundancy divides information about the system into three parts: classical (redundant); purely quantum; and the borderline, undifferentiated or ``nonredundant, information.
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