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arXiv:1201.4975

Classicality from zero discord for continuous-variables bipartite systems

M. Arsenijević, J. Jeknić-Dugić, M. Dugić

Published Jan 24, 2012• 0 citations
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Abstract

Quantum information resources quantified by non-zero discord are ubiquitous for the continuous-variables bipartite systems. Complementary to this, we formally construct a model characterized by zero two-way discord for arbitrarily long time interval. The model is classical in the sense it does not support quantum information processing. We point out some interesting physical features of the model.

DOI
10.48550/arxiv.1201.4975

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Quantum information resources quantified by non-zero discord are ubiquitous for the continuous-variables bipartite systems. Complementary to this, we formally construct a model characterized by zero two-way discord for arbitrarily long time interval. The model is classical in the sense it does not support quantum information processing. We point out some interesting physical features of the model.
Recent observation that almost all quantum states bear non-classical correlations [A. Ferraro et al, Phys. Rev. A 81, 052328 (2010)] may seem to imply that the Markovian bipartite systems are practically deprived of zero discord states. Nevertheless, complementary to the result of Ferraro et al, we construct a model of a Markovian bipartite system providing zero discord for arbitrary long time interval, that we term 'Markovian classicality'. Our model represents a matter-of-principle formal proof, i.e. a sufficient condition for the, otherwise not obvious, existence of Markovian classicality. Interestingly enough, we are not able to offer any alternative to the model. Physical relevance of the model is twofold. First, the model is in intimate relation to the topics of quantum information locality, quantum discord saturation and quantum decorrelation. Second, the model is of the general physical interest. It pertains to a specific structure (decomposition into parts/subsystems) of a composite system, not to a special physical kind of composite systems. Being a characteristic of a structure, by definition, the model of Markovian classicality is not a model of sudden death of discord. We emphasize wide-range implications of our results.
Quantum discord measures the total non-classical correlations in a composite quantum system. As a possible resource for the classically non-achievable tasks, amount of quantum discord is crucial for efficient performance of the quantum technology tasks. Zero discord means the absence of the required resources. For a wide class of the bipartite open quantum systems, initial nonzero discord is known practically never goes to zero, except asymptotically. However, if initial discord equals zero, there remains the possibility to remain zero for the finite time intervals for certain Markovian models of open systems-that we call Markovian classicality. In this paper we search for the models that allow for Markovian classicality. We point out a general model that represents a matter-of-principle formal proof, i.e. a sufficient condition for the, otherwise not obvious, existence of Markovian classicality. Physical relevance of the model is twofold. First, the model is in intimate relation to the topics of quantum information locality, quantum discord saturation and quantum decorrelation. Second, the model is of the general physical interest. It pertains to a specific structure (decomposition into parts/subsystems) of a composite system, not to a special kind of composite system. Being a characteristic of a structure, by definition, the model of Markovian classicality is not a model of sudden death of discord. We emphasize wide-range implications of our results.
Modern quantum information theory provides new tools for investigating the decoherence-induced "classicality" of open quantum systems. Recent observation that almost all quantum states bear non-classical correlations [A. Ferraro {\it et al}, Phys. Rev. A {\bf 81}, 052318 (2010)] distinguishes the zero-discord classicality essentially as a pathology of the Markovian bipartite-systems realm. Nevertheless, we formally construct such a classical model and its variant that represents a matter-of-principle formal proof, i.e. a sufficient condition for the, otherwise not obvious, existence of the Markovian zero-discord classicality. A need for the more elaborate and more systematic search for the alternative such models reveals we are still learning about the very meaning of "classicality" in the realm of open quantum systems.