Abstract
We apply the modified Brodutch and Modi method of constructing geometric measures of correlations to obtain analytical expressions for measurement-induced geometric classical and quantum correlations based on the Hellinger distance for two-qubit Bell diagonal states. Moreover, we study dynamics of the classical and quantum correlations for these states under decoherence induced by the action of bit flip, bit-phase flip, phase flip, depolarizing and generalized amplitude damping local quantum channels and identify all possible types of the decoherence dynamics. In particular, we show that these correlations exhibit freezing, sudden change and sudden transition between classical and quantum decoherence phenomena.
Highlights
In quantum information science, the problem of classification and quantification of correlations present in composite quantum systems has been extensively investigated in the last few decades [1,2,3,4]
We apply the modified Brodutch and Modi method of constructing geometric measures of correlations [22,23] to obtain analytical expressions for measurement-induced geometric classical and quantum correlations based on the Hellinger distance for two-qubit Bell diagonal states
Let us note that the conditions for all possible types of dynamics of measurementinduced geometric classical and quantum correlations based on the Hellinger distance for two-qubit Bell diagonal states under the action of bit-phase flip and phase flip local quantum channels can be obtained from the conditions presented in Sect. 3.1 by swapping c1 with c2 and c1 with c3, respectively
Summary
The problem of classification and quantification of correlations present in composite quantum systems has been extensively investigated in the last few decades [1,2,3,4]. The problems with geometric quantum discord based on the Schatten 2-norm have highlighted the need for a general method of constructing bona fide measures of correlations within the information-theoretic paradigm. It has been shown that the Brodutch and Modi method should be modified as in the case of measurement-induced classical and quantum correlations based on the trace distance for two-qubit Bell diagonal states one of the two possible strategies results in the non-uniqueness of classical correlations [23]. We apply the modified Brodutch and Modi method to solve the open problem of determining measurement-induced classical and quantum correlations based on the Hellinger distance for two-qubit Bell diagonal states [3]. We identify all possible types of dynamics of the classical and quantum correlations under decoherence induced by the action of these quantum channels
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