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Chinese Physics B

Comparative investigation of freezing phenomena for quantum coherence and correlations

Lian-Wu Yang, Wei Han, Yun‐Jie Xia

Published Apr 1, 2018• 3 citations
Publisher

Abstract

We show that the freezing phenomenon, exhibited by a specific class of two-qubit state under local nondissipative decoherent evolutions, is a common feature of the relative entropy measure of quantum coherence and correlation. All those measurement outcomes, preserve a constant value in the considered noisy channels, but the condition, property and mechanism of the freezing phenomenon for quantum coherence are different from those of the quantum correlation.

DOI
10.1088/1674-1056/27/4/040302

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We show that the freezing phenomenon, exhibited by a specific class of two-qubit state under local nondissipative decoherent evolutions, is a common feature of the relative entropy measure of quantum coherence and correlation. All those measurement outcomes, preserve a constant value in the considered noisy channels, but the condition, property and mechanism of the freezing phenomenon for quantum coherence are different from those of the quantum correlation.
We show that the phenomenon of frozen discord, exhibited by specific classes of two-qubit states under local nondissipative decoherent evolutions, is a common feature of all known bona fide measures of general quantum correlations. All those measures, despite inducing typically inequivalent orderings on the set of nonclassically correlated states, return a constant value in the considered settings. Every communication protocol that relies on quantum correlations as a resource will run with a performance completely unaffected by noise in the specified dynamical conditions. We provide a geometric interpretation of this phenomenon.
We analyze under which dynamical conditions the coherence of an open quantum system is totally unaffected by noise. For a single qubit, specific measures of coherence are found to freeze under different conditions, with no general agreement between them. Conversely, for an N-qubit system with even N, we identify universal conditions in terms of initial states and local incoherent channels such that all bona fide distance-based coherence monotones are left invariant during the entire evolution. This finding also provides an insightful physical interpretation for the freezing phenomenon of quantum correlations beyond entanglement. We further obtain analytical results for distance-based measures of coherence in two-qubit states with maximally mixed marginals.
We provide necessary and sufficient conditions for freezing of quantum correlations as measured by quantum discord and quantum work deficit in the case of bipartite as well as multipartite states subjected to local noisy channels. We recognize that inhomogeneity of the magnetizations of the shared quantum states plays an important role in the freezing phenomena. We show that the frozen value of the quantum correlation and the time interval for freezing follow a complementarity relation. For states which do not exhibit ``exact'' freezing, but can be frozen ``effectively,'' by having a very slow decay rate with suitable tuning of the state parameters, we introduce an index---the freezing index---to quantify the goodness of freezing. We find that the freezing index can be used to detect quantum phase transitions and discuss the corresponding scaling behavior.
Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show that all distance functions, which respect natural assumptions of invariance under transposition, convexity, and contractivity under quantum channels, give rise to geometric quantifiers of quantum correlations which exhibit the peculiar freezing phenomenon, i.e., remain constant during the evolution of a paradigmatic class of states of two qubits each independently interacting with a non-dissipative decohering environment. Our results demonstrate from first principles that freezing of geometric quantum correlations is independent of the adopted distance and therefore universal. This finding paves the way to a deeper physical interpretation and future practical exploitation of the phenomenon for noisy quantum technologies.
Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show that all distance functions, which respect natural assumptions of invariance under transposition, convexity, and contractivity under quantum channels, give rise to geometric quantifiers of quantum correlations which exhibit the peculiar freezing phenomenon, i.e., remain constant during the evolution of a paradigmatic class of states of two qubits each independently interacting with a non-dissipative decohering environment. Our results demonstrate from first principles that freezing of geometric quantum correlations is independent of the adopted distance and therefore universal. This finding paves the way to a deeper physical interpretation and future practical exploitation of the phenomenon for noisy quantum technologies.
Abstract. Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. We show that all distance functions, which respect natural assumptions of invariance under transposition, convexity, and contractivity under quantum channels, give rise to geometric quantifiers of quantum correlations which exhibit the peculiar freezing phenomenon, i.e., remain constant during the evolution of a paradigmatic class of states of two qubits each independently interacting with a non-dissipative decohering environment. Our results demonstrate from first principles that freezing of geometric quantum correlations is independent of the adopted distance and therefore universal. This finding paves the way to a deeper physical interpretation and future practical exploitation