Freezing of quantum correlations under local decoherence

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.

Sudden change of geometric quantum discord in finite temperature reservoirs

“…Moreover, when considering their evolution for open quantum system, quantum discord and entanglement also exhibit distinct singular behaviors. For instance, quantum discord is more robust against decoherence than entanglement [18][19][20], it is immune to certain quantum noises during certain time intervals [21][22][23][24][25], and therefore exhibits the frozen behavior which is impossible for entangle- * Electronic address: mingliang0301@163.com ment. Quantum discord exhibits sudden changes (SCs) due to the optimization procedure involved in its definition [26][27][28][29][30][31][32], while entanglement undergoes sudden death [33] which does not exist for quantum discord.…”

Reducing computational complexity of quantum correlations

“…The subset, in the present case, consists of the projection measurements corresponding to the three Pauli matrices, σ x , σ y , and σ z . Curiously, the assumption that QD can be optimized over this subset for the entire class of such states results only in a small absolute error in the case of those states where the assumption is not valid [27,29]. This property also allows one to determine closed form for QD for the entire class of such two-qubit states within the margin of small absolute error in calculation [27][28][29].…”

“…Since completely analytical forms of QD and QWD are not yet available [23], numerical techniques need to be employed, and our methodology show a path to handle them analytically. See [28,29] in this respect.…”

“…Also, the existence of such subsets has the potential to be operationally as well as energetically advantageous in experimental determination of the QD and similar measures for a given quantum state. However, the investigation of the existence of such special subsets of allowed local projectors in the computation of quantum correlations like QD and QWD, as of now, are confined only to special classes of quantum states in C 2 ⊗ C 2 systems [27][28][29]. A natural question that arises is whether such subsets of local projectors can exist for general bipartite quantum states.…”

“…A number of recent numerical studies have shown that for a large fraction of a very special class of two-qubit states, QD can always be calculated by performing the optimization over only a small subset of the complete set of local projection measurements [27,29], thereby reducing the computational difficulty to a great extent. These states are constructed of the three diagonal correlators of the correlation matrix, and any one of the three magnetizations, which is similar for both the qubits.…”