Creating quantum correlations in generalized entanglement swapping

Abstract

We study how different types of quantum correlations can be established as the consequence of a generalized entanglement swapping protocol where, starting from two Bell pairs (1,2) and (3,4), a general quantum measurement [denoted by a positive operator-valued measure (POVM)] is performed on the pair (2,3), which results in creating quantum correlation in (1,4) shared between two spatially separated observers. Contingent upon using different kinds of POVMs, we show generation or destruction of different quantum correlations in the pairs (1,4), (1,2), and (3,4). This thus reflects nontrivial transfer of quantum correlations from the pairs (1,2) and (3,4) to the pair (1,4). As an offshoot, this paper provides an operational tool to generate different types of single parameter families of quantum correlated states [for example, entangled but not Einstein-Podolsky-Rosen (EPR) steerable, or EPR steerable but not Bell nonlocal, or Bell nonlocal] by choosing different quantum measurements in the basic entanglement swapping setup. We further extend our paper by taking mixed initial states shared by the pairs (1,2) and (3,4). Finally, we study network nonlocality in our scenario. Here, we find the appropriate POVM measurement for which the generated correlation demonstrates or does not demonstrate network nonlocality for the whole range of the measurement parameter.

Quantum correlations in a chain-type quantum network

“…where the value of i is the same as that of equation (7), (6) reduces to the related result in [31]. Hence, our result is a natural generalization of that in [31].…”

“…As a result of their significance, much research has been devoted to investigating quantum correlations generated by quantum networks, such as Bell nonlocality in networks [27], network entanglement [28], network steering [29] and network coherence [30], which are different from conventional quantum correlations. In contrast to the above works, which are focused on examining some specific quantum correlations pertaining to quantum networks, the authors in [31] recently studied the conventional quantum correlations of all post-measurement states in a generalized entanglement swapping protocol. In this protocol, they characterized the variations of quantum correlations of all postmeasurement states with respect to the initial quantum states and quantum measurements with parameters.…”