Local available quantum correlations of non-symmetric X states

TL;DR

This paper derives an explicit formula for local available quantum correlations in non-symmetric 2-qubit X states and examines their behavior under local amplitude damping channels, showing LAQC's monotonicity under LOCC.

Contribution

It provides the first simple analytic expression for LAQC in non-symmetric X states and extends previous results to complete the analytical characterization of LAQC for all 2-qubit X states.

Findings

LAQC quantifier derived analytically for non-symmetric X states

LAQC remains unchanged under local amplitude damping channels in tested cases

LAQC is monotonic under LOCC, unlike quantum discord in some scenarios

Abstract

Local available quantum correlations (LAQC), as defined by Mundarain et al., are analyzed for non-symmetric 2-qubit X states, that is, X-states that are not invariant under the exchange of subsystems and therefore have local Bloch vectors whose norms are different. A simple analytic expression for their LAQC quantifier is obtained. As an example, we analyze the local application of the amplitude damping channel for Werner states and general X states. Although this local quantum channel can create quantum discord in some cases, no such outcome is possible for LAQC, which hints toward their monotonicity under LOCC operations. This work, along with our previous result for so-called symmetric and anti-symmetric X states, completes the pursuit of exact analytical expressions for the LAQC quantifier for 2-qubit X states.