Violation of Bell Monogamy Relations

TL;DR

This work investigates how Bell nonlocality is shared among subsystems in multipartite, permutation-symmetric states, with a focus on $W$ states. The authors show that Bell-CHSH monogamy relations are respected by reduced states of $W$ states, but can be violated by local filtering operations, providing analytic thresholds for two-qubit reductions and numerical evidence for higher-qubit reductions. Extending to multipartite Bell inequalities (e.g., Mermin, Svetlichny, DDA, minimal-scenario), they find that monogamy relations hold before filtering, yet can be breached after filtering, with the violation thresholds scaling roughly as $h<\sqrt{2(\sqrt{2}-1)/(N-M)}$. These results reveal a subtle vulnerability of Bell monogamy under local operations and suggest the need for more robust monogamy formulations applicable to nonlocality sharing in complex quantum networks.

Abstract

The entangled multipartite systems, specially in pure states, exhibit the phenomenon entanglement monogamy. Such systems also display the phenomenon of Bell nonlocality. Like entanglement monogamy relations, there are Bell monogamy relations. These relations suggest a sharing of nonlocality across the subsystems. The nonlocality, as characterized by Bell inequalities, of one subsystem limits the nonlocality exhibited by another subsystem. We show that the Bell monogamy relations can be violated by using local filtering operations. We consider permutation-symmetric multipartite pure states, in particular $W$ states, to demonstrate the violation.

Figures (1)

• Figure 1: Maximum filter parameter ($h$) required for violation of Facet inequality of $M=3$ qubit reduced state from $N$ qubit $W$ state.