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 trace distance for two-qubit X states. Moreover, we study continuity of the classical and quantum correlations for these states. In particular, we show that these correlations may not be continuous.
Highlights
In quantum information science, the problem of classification and quantification of correlations present in quantum systems has been extensively studied over the past few decades [1,2,3,4,5]
We apply the modified Brodutch and Modi method to obtain measurement-induced geometric classical and quantum correlations based on the trace distance for two-qubit X states using two possible strategies of constructing bona fide measures of correlations
The above results regarding to measurement-induced geometric quantum correlations based on the trace distance for two-qubit X states can be summarized as follows:
Summary
The problem of classification and quantification of correlations present in quantum systems has been extensively studied over the past few decades [1,2,3,4,5]. The problem with geometric quantum discord based on the Schatten 2-norm has emphasized the need for a general method of constructing bona fide measures of correlations under the information-theoretic paradigm. It was shown that the Brodutch and Modi method should be modified as in the case of measurement-induced geometric classical and quantum correlations based on the trace distance for two-qubit Bell diagonal states one of two possible strategies results in the non-uniqueness of classical correlations [29]. We apply the modified Brodutch and Modi method to obtain measurement-induced geometric classical and quantum correlations based on the trace distance for two-qubit X states using two possible strategies of constructing bona fide measures of correlations. It is assumed without loss of generality that c12 ≥ c22 since the sign of ρ14 in the density matrix (5) can always be changed by a local unitary transformation [32]
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