Optimal measurements to access classical correlations of two-qubit states

Abstract

We analyze the optimal measurements to access classical correlations in arbitrary two-qubit states. Two-qubit states can be transformed into the canonical forms via local unitary operations. For the canonical forms, we investigate the probability distribution of the optimal measurements. The probability distribution of the optimal measurements is found to be centralized in the vicinity of a specific von Neumann measurement, which we call the maximal-correlation-direction measurement (MCDM). We prove that, for the states with zero discord and maximally mixed marginals, the MCDM is the optimal measurement. Furthermore, we give an upper bound of quantum discord based on the MCDM, and investigate its performance for approximating the quantum discord.

Revisiting Quantum Discord for Two-Qubit X States: The Error Bound to an Analytical Formula

“…(21) [15] and Eq. (22) [18] does not change dramatically according to the measurement setting. Table I shows the quantum discord of 3 element POVM, that of 2 projective measurements and that of measurement obtained by Ali et al(δ 2 ) respectively.…”

“…Quantum discord for a Bell-diagonal state was analytically obtained [10]. Much research has had a focus on finding the quantum discord of the X state [12][13][14][15][16][17][18].…”

“…The optimality for 3 element POVM can be found by a triangle formed by the direction vectors. By using 3 element POVM, we numerically obtained the quantum discord to the quantum state considered in [15,18] and compared it with the result of [15].…”

Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks

“…To see how to calculate the QFI or FS, we take the X state as an example, which is defined as [27,28,29,30,31] …”

Thermally generated long-lived quantum correlations for two atoms trapped in fiber-coupled cavities

“…For example, by using the concepts of mutual information and quantum discord (QD) the quantum correlations may be distinguished from the classical ones. Further the QD could be compared to the entanglement of formation (E) [7] in order to find if the system is in a quantum inseparable state (entangled), or in a separable state with quantum correlations, sucha as QD [8][9][10][11]. Such an analysis is considered in this paper.…”