Local available quantum correlations of X states: The symmetric and anti-symmetric cases

TL;DR

This paper derives exact analytical expressions for local available quantum correlations in symmetric and anti-symmetric 2-qubit X states, compares them with other quantum correlations, and studies their robustness under Markovian decoherence.

Contribution

It provides the first analytical formulas for LAQC in symmetric and anti-symmetric X states and analyzes their behavior under decoherence.

Findings

LAQC expressions are derived analytically for symmetric and anti-symmetric X states.

LAQC does not exhibit sudden death under amplitude damping decoherence.

LAQC comparison shows different robustness compared to concurrence and quantum discord.

Abstract

Local available quantum correlations (LAQC), as defined by Mundarain et al., are analyzed for 2-qubit X states with local Bloch vectors of equal magnitude. Symmetric X-states are invariant under the exchange of subsystems, hence having the same {local} Bloch vector. On the other hand, anti-symmetric X states have {local} Bloch vectors with an equal magnitude but opposite direction {(anti-parallel)}. In both cases, we obtain exact analytical expressions for their LAQC quantifier. We present some examples and compare this quantum correlation to concurrence and quantum discord. We have also included Markovian decoherence, with Werner states under amplitude damping decoherence. As is the case for depolarization and phase damping, no sudden death behavior occurs for the LAQC of these states with this quantum channel.