<p>Although introduced for entanglement, quantum repeaters and swapping protocols have been analyzed for other quantum correlations (QC), such as quantum discord. Introduced by Mundarain and Ladrón de Guevara [<CitationRef CitationID="CR43">43</CitationRef>], local-available quantum correlations (LAQC) are a type of residual quantum correlation mostly overlooked in the literature. Recently, Bellorin et al. [<CitationRef CitationID="CR44">44</CitationRef>, <CitationRef CitationID="CR45">45</CitationRef>] obtained exact analytical results for its measure for general 2-qubit X states. Building on those results, we analyzed the behavior of this measure in a standard quantum correlation swapping (QCS) protocol, focusing on 2-qubit X states as the initial 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, in general, have non-zero LAQC. Using its properties, we establish the conditions required for the final state in the QCS scheme having a non-null LAQC measure. We illustrate these results by analyzing six relevant families of one-parameter 2-qubit X states. Within those examples, we included mixed states that result in a separable state but a non-zero LAQC measure. We also included a separable quantum-correlated mixed state that remains separable and quantum correlated after the QCS scheme.</p>

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Local-Available Quantum Correlations in a Standard Quantum Correlation Swapping Scheme

  • Hermann L. Albrecht

摘要

Although introduced for entanglement, quantum repeaters and swapping protocols have been analyzed for other quantum correlations (QC), such as quantum discord. Introduced by Mundarain and Ladrón de Guevara [43], local-available quantum correlations (LAQC) are a type of residual quantum correlation mostly overlooked in the literature. Recently, Bellorin et al. [44, 45] obtained exact analytical results for its measure for general 2-qubit X states. Building on those results, we analyzed the behavior of this measure in a standard quantum correlation swapping (QCS) protocol, focusing on 2-qubit X states as the initial 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, in general, have non-zero LAQC. Using its properties, we establish the conditions required for the final state in the QCS scheme having a non-null LAQC measure. We illustrate these results by analyzing six relevant families of one-parameter 2-qubit X states. Within those examples, we included mixed states that result in a separable state but a non-zero LAQC measure. We also included a separable quantum-correlated mixed state that remains separable and quantum correlated after the QCS scheme.