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