Quantum discord of two-qubitXstates

Abstract

Quantum discord provides a measure for quantifying quantum correlations beyond entanglement and is very hard to compute even for two-qubit states because of the minimization over all possible measurements. Recently a simple algorithm to evaluate the quantum discord for two-qubit X-states is proposed by Ali, Rau and Alber [Phys. Rev. A 81, 042105 (2010)] with minimization taken over only a few cases. Here we shall at first identify a class of X-states, whose quantum discord can be evaluated analytically without any minimization, for which their algorithm is valid, and also identify a family of X-states for which their algorithm fails. And then we demonstrate that this special family of X-states provides furthermore an explicit example for the inequivalence between the minimization over positive operator-valued measures and that over von Neumann measurements. For an important family of two-qubit states, the so called X-states [25], an algorithm has been proposed to calculate their quantum discord with minimization taken over only a few simple cases [26], which is unfortunately impeded by a counter example [27]. In this paper we shall at first identify a vast class of X-states, whose quantum discord can be evaluated analytically without any minimization at all, for which their algorithm is valid, and also identify a family of X-states X m , the so-called maximally discordant mixed states [24], for which the above mentioned algorithm fails. And then for this family of Xstates X m we construct a POVM showing that the quantum discord obtained by minimization over all POVMs is strictly smaller than that over all possible von Neumann measurements.For a given quantum state ̺ of a composite system AB the total amount of correlations, including classical and quantum correlations, is quantified by the quantum mutual information I(ρ) = S(̺ A ) + S(̺ B ) − S(̺) where S(̺) = −Tr(̺ log 2 ̺) denotes the von Neumann entropy and ̺ A , ̺ B are reduced density matrices for subsystem A, B respectively. An alternative version of the mutual information can be defined aswhere the minimum is taken over all possible POVMs {E defines the quantum discord that quantifies the quantum correlation. Also the minimum in Eq.(1) can be taken over all von Neumann measurements [3] and we

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

“…[12] tried to find an analytic formula of quantum discord to X state. However, it is known that the result of [12] holds only to special X state [13]. Fanchini et.…”

“…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].…”

Superdense Coding with Uniformly Accelerated Particle

“…(18), and employing the approach explained in Refs. [27,28], quantum discord is calculated for which Fig. 2 shows its behavior as a function of r. It is clear, that four quantities, probability of success, superdense coding capacity, logarithmic negativity and quantum discord for superdense coding with accelerated particle, in single mode approximation, are descending functions of r.…”

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] …”