Local-available quantum correlation swapping in one-parameter X states

TL;DR

This paper investigates local-available quantum correlations (LAQC) swapping in one-parameter X states, revealing conditions for non-zero LAQC in final states and highlighting its potential as a quantum resource.

Contribution

It provides the first analysis of LAQC swapping in 2-qubit X states, establishing conditions for non-zero LAQC and exploring its resource potential.

Findings

Non-zero LAQC can be achieved with entangled measurements.

Certain X states retain LAQC even when entanglement is absent.

LAQC can serve as a genuine quantum resource.

Abstract

Although introduced for entanglement, quantum repeaters and swapping protocols have been analyzed for other quantum correlations (QC), such as quantum discord. In 2015, Mundarain and Ladr\'on de Guevara [Quantum Inf. Process. 14, 4493 (2015)] introduced local-available quantum correlations (LAQC), which are a promising yet understudied quantum correlation. Recently, Bellorin et al. [Int. J. Mod. Phys. B 36, 22500990 (2022), Int. J. Mod. Phys. B 36, 2250154 (2022)] obtained exact analytical results for the LAQC quantifier of general 2-qubit X states. Building up from those results, we analyzed the LAQC swapping for 2-qubit X states. As expected, we find that if the initial states are non-classical and the one used for the projective measurement is entangled, the final state will generally have non-zero LAQC. Using the properties of this quantum correlation, we establish the conditions for a QCS scheme that leads to a final state with a non-zero LAQC measure. We illustrate these results by analyzing five families of one-parameter 2-qubit X states, including families where the projective measure leads to a separable state, but whose LAQC measure is non-zero. This feature opens the possibility for this quantum correlation to be considered a genuine resource in quantum information technology.