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arXiv:1409.2096 · Physical Review A

Freezing of quantum correlations under local decoherence

Titas Chanda, Amit Kumar Pal, Anindya Biswas, Aditi Sen, Ujjwal Sen

Published Jun 16, 2015• 43 citations
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Abstract

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.

DOI
10.1103/physreva.91.062119

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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.
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.
The total correlation in a bipartite quantum system is measured by the quantum mutual information I\mathcal{I}I, which consists of quantum discord and classical correlation. However, recent results in quantum information show that coherence, which is a part of total correlation, is more general and more fundamental. The role of coherence in quantum resource theory is worthwhile to investigate. We first study the relationship between quantum discord and coherence by decreasing the difference between them. Then, we consider the dynamics of quantum discord, classical correlation, and quantum coherence under incoherent quantum channels. It is found that coherence indicates the behavior of quantum discord (classical correlation) for times t<t‾t<\overline{t}t<t, and indicates the behavior of classical correlation (quantum discord) for times t>t‾t>\overline{t}t>t. Moreover, the coherence freeze and decay characterize the quantum discord and classical correlation freeze and decay, respectively.
A special emphasis is devoted to the concept of local quantum uncertainty as an indicator of quantum correlations. We study quantum discord for a class of two-qubit states parametrized by two parameters. Quantum discord based on local quantum uncertainty, von Neumann entropy and trace distance (Schatten 1-norm) are explicitly derived and compared. The behavior of quantum correlations, quantified via local quantum uncertainty, under decoherence effects is investigated. We show that the discordlike local quantum uncertainty exhibits the possibility of freezing behavior during its evolution.
We investigate the freezing phenomenon of quantum discord occurring in phase damping noise processes. By relating the expression of the time variation of the discord to the convex function of relative entropy, we obtain the necessary and sufficient conditions of the phenomenon for standard Bell-diagonal states. These conditions are applicable also to the phenomenon occurring in a non-Markovian dephasing process. Moreover, we show that the same condition and phenomenon coincide in an unusual sort of Bell-diagonal states beyond the standard form.
We consider a process to create quasi–long-range quantum discord between the non-interacting end spins of a quantum spin chain, with the end spins weakly coupled to the bulk of the chain. The process is not only capable of creating long-range quantum correlation but the latter remains frozen, when certain weak end-couplings are adiabatically varied below certain thresholds. We term this phenomenon as adiabatic freezing of quantum correlation. We observe that the freezing is robust to moderate thermal fluctuations and is intrinsically related to the cooperative properties of the quantum spin chain. In particular, we find that the energy gap of the system remains frozen for these adiabatic variations, and moreover, considering the end spins as probes, we show that the interval of freezing can detect the anisotropy transition in quantum XY spin chains. Importantly, the adiabatic freezing of long-range quantum correlations can be simulated with contemporary experimental techniques.