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arXiv:2101.09186 · Physical Review Letters

Comment on “Strong Quantum Darwinism and Strong Independence Are Equivalent to Spectrum Broadcast Structure”

Alexandre Feller, Benjamin Roussel, Irénée Frérot, Pascal Degiovanni

Published May 7, 2021• 7 citations
arXivHTMLPDF

Abstract

In a recent Letter [Phys. Rev. Lett. 122, 010403 (2019)], an equivalence is proposed between the so-called Spectrum Broadcast Structure for a system-multienvironment quantum state, and the conjunction of two information-theory notions: (a) Strong Quantum Darwinism; and (b) Strong Independence. Here, we show that the mathematical formulation of condition (b) by the authors (namely, the pairwise independence of the fragments of the environment, conditioned on the system), is necessary but not sufficient to ensure the equivalence. We propose a simple counter-example, together with a strengthened formulation of condition (b), ensuring the equivalence proposed by the authors.

DOI
10.1103/physrevlett.126.188901

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Reply to Comment on "Strong Quantum Darwinism and Strong Independence are Equivalent to Spectrum Broadcast Structure"

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In a recent comment [Feller et. al, arXiv:2101.09186] on our Letter [Phys. Rev. Lett. 122, 010403 (2019)], Feller et. al identified a mistake in our mathematical expression of "strong independence" for states that satisfy Spectrum Broadcast Structure. We concede that we wrote a mathematical condition that is necessary but not sufficient. However, we used the original and correct qualitative definition for "strong independence" throughout the paper and in our proofs, therefore the proofs and statements, aside from the aforementioned mathematical expression, remain correct.

arXiv:2101.10756•Jan 26, 2021•0 citations

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How the objective everyday world emerges from the underlying quantum behavior of its microscopic constituents is an open question at the heart of the foundations of quantum mechanics. Quantum Darwinism and spectrum broadcast structure are two different frameworks providing key insight into this question. Recent works, however, indicate these two frameworks can lead to conflicting predictions on the objectivity of the state of a system interacting with an environment. Here, we provide a resolution to this issue by defining strong quantum Darwinism and proving that it is equivalent to spectrum broadcast structure when combined with strong independence of the subenvironments. We further show that strong quantum Darwinism is sufficient and necessary to signal state objectivity without the requirement of strong independence. Our Letter unveils the deep connection between strong quantum Darwinism and spectrum broadcast structure, thereby making fundamental progress toward understanding and solving the emergence of classicality from the quantum world. Together they provide us a sharper understanding of the transition in terms of state structure, geometry, and quantum and classical information.

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•Mar 2, 2018•0 citations
In a recent Letter [Phys. Rev. Lett. 122, 010403 (2019)], an equivalence is proposed between the so-called Spectrum Broadcast Structure for a system-multienvironment quantum state, and the conjunction of two information-theory notions: (a) Strong Quantum Darwinism; and (b) Strong Independence. Here, we show that the mathematical formulation of condition (b) by the authors (namely, the pairwise independence of the fragments of the environment, conditioned on the system), is necessary but not sufficient to ensure the equivalence. We propose a simple counter-example, together with a strengthened formulation of condition (b), ensuring the equivalence proposed by the authors.
In a recent comment [Feller et. al, arXiv:2101.09186] on our Letter [Phys. Rev. Lett. 122, 010403 (2019)], Feller et. al identified a mistake in our mathematical expression of "strong independence" for states that satisfy Spectrum Broadcast Structure. We concede that we wrote a mathematical condition that is necessary but not sufficient. However, we used the original and correct qualitative definition for "strong independence" throughout the paper and in our proofs, therefore the proofs and statements, aside from the aforementioned mathematical expression, remain correct.
How the objective everyday world emerges from the underlying quantum behavior of its microscopic constituents is an open question at the heart of the foundations of quantum mechanics. Quantum Darwinism and spectrum broadcast structure are two different frameworks providing key insight into this question. Recent works, however, indicate these two frameworks can lead to conflicting predictions on the objectivity of the state of a system interacting with an environment. Here, we provide a resolution to this issue by defining strong quantum Darwinism and proving that it is equivalent to spectrum broadcast structure when combined with strong independence of the subenvironments. We further show that strong quantum Darwinism is sufficient and necessary to signal state objectivity without the requirement of strong independence. Our Letter unveils the deep connection between strong quantum Darwinism and spectrum broadcast structure, thereby making fundamental progress toward understanding and solving the emergence of classicality from the quantum world. Together they provide us a sharper understanding of the transition in terms of state structure, geometry, and quantum and classical information.
Quantum Darwinism and spectrum broadcast structure describe the emergence of objectivity in quantum systems. However, it is unclear whether these two frameworks lead to consistent predictions on the objectivity of the state of a quantum system in a given scenario. In this paper, we jointly investigate quantum Darwinism and spectrum broadcasting, as well as the subdivision of quantum Darwinism into accessible information and quantum discord, in a two-level system interacting with an NNN-level environment via a random matrix coupling. We propose a partial trace method to suitably and consistently partition the effective NNN-level environment and compare the predictions with those obtained using the partitioning method proposed by Perez [Phys. Rev. A 81, 052326 (2010)]. We find that quantum Darwinism can apparently emerge under the Perez trace even when spectrum broadcast structure does not emerge, and the majority of the quantum mutual information between system and environment fractions is in fact quantum in nature. This work therefore shows there can be discrepancies between quantum Darwinism and the nature of information and spectrum broadcast structure.
Quantum mechanics is one of the most successful theories, correctly predicting huge class of physical phenomena. Ironically, in spite of all its successes, there is a notorious problem: how does Nature create a ''bridge'' from fragile quanta to the robust, objective world of everyday experience? It is now commonly accepted that the most promising approach is the Decoherence Theory, based on the system-environment paradigm. To explain the observed redundancy and objectivity of information in the classical realm, Zurek proposed to divide the environment into independent fractions and argued that each of them carries a nearly complete classical information about the system. This Quantum Darwinism model has nevertheless some serious drawbacks: i) the entropic information redundancy is motivated by a priori purely classical reasoning; ii) there is no answer to the basic question: what physical process makes the transition from quantum description to classical objectivity possible? Here we prove that the necessary and sufficient condition for objective existence of a state is the spectrum broadcasting process, which, in particular, implies Quantum Darwinism. We first show it in general, using multiple environments paradigm, a suitable definition of objectivity, and Bohr's notion of non-disturbance, and then on the emblematic example for Decoherence Theory: a dielectric sphere illuminated by photons. We also apply Perron-Frobenius Theorem to show a faithful, ''decoherence-free'' form of broadcasting. We suggest that the spectrum broadcasting might be one of the foundational properties of Nature, which opens a ''window'' for life processes.
The problem of objectivity, i.e. how to explain on quantum grounds the objective character of the macroscopic world, is one of the aspects of the celebrated quantum-to-classical transition. Initiated by W. H. Zurek and collaborators, this problem gained some attention recently with several approaches being developed. The aim of this paper is to compare three of them: quantum Darwinism, Spectrum Broadcast Structures, and strong quantum Darwinism. I will concentrate solely on foundations, analyzing how the three approaches realize the idea of objectivity and how they are related to each other. I will also briefly comment on the recent quantum Darwinism experiments.
Quantum Darwinism and spectrum broadcast structure describe the emergence of objectivity in quantum systems. However, it is unclear whether these two frameworks lead to consistent predictions on the objectivity of the state of a quantum system in a given scenario. In this paper, we jointly investigate quantum Darwinism and spectrum broadcasting, as well as the subdivision of quantum Darwinism into accessible information and quantum discord, in a two-level system interacting with an NNN-level environment via a random matrix coupling. We propose a novel partial trace method to suitably and consistently partition the effective NNN-level environment, and compare the predictions with those obtained using the partitioning method proposed by Perez [Phys. Rev. A 81, 052326 (2010)]. We find that Quantum Darwinism can apparently emerge even when spectrum broadcast structure does not emerge, and the majority of the quantum mutual information between system and environment fractions is in fact quantum in nature. This work therefore shows there can be discrepancies between quantum Darwinism, and the nature of information and spectrum broadcast structure.