Creating quantum correlations in generalized entanglement swapping

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 or 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 non-trivial transfer of quantum correlations from the pairs (1, 2) and (3, 4) to the pair (1, 4). As an offshoot, this study provides an operational tool to generate different types of single parameter families of quantum correlated states (for example, entangled but not 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 study 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 out appropriate POVM measurement for which the generated correlation demonstrates/does not demonstrate network nonlocality for the whole range of the measurement parameter.
Comment: Accepted for publication in Physical Review A, Close to final version