Hilbert–Schmidt Measure of Pairwise Quantum Discord for Three-Qubit X States

Abstract

The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system. Analytical expressions of geometric quantum discord are derived. A particular attention is devoted to two special classes of three-qubit X states. They include three-qubit states of W, GHZ and Bell type. We also discuss the monogamy property of geometric quantum discord in some mixed three-qubit systems. 1

The dynamic behaviors of local quantum uncertainty for three-qubit X states under decoherence channels

“…This unexpected result was reported in [25]. Furthermore, now it is well established that geometric discord based on Hilbert-Schmidt [26,27] is not a faithful measure of quantum correlations [28]. In fact, this quantifier can increase under local quantum operations acting on the unmeasured qubit.…”

“…In this case also the matrix W , whose elements are given by (26), is diagonal. The diagonal elements write…”

“…where i and j take the values 1, 2, 3. To evaluate w ij (26), we write the matrix √ ρ 123 in the Fano-…”

“…The correlation tensor elements T χδη are given in the appendix. After some algebra, one shown that the matrix elements (26) are explicitly given by…”

Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord Quantification

“…The calculation of quantum discord functions (QD) usually involves hard optimization problems [46,47]. In the last few years, a large amount of effort have been dedicated towards computing QD analytically, with success being obtained mostly for low dimensional quantum systems [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65]. Although not meeting all the required properties for a bona fide QD quantifier [66], the Hilbert-Schmidt discord (HSD) [67],…”