Unmasking the Polygamous Nature of Quantum Nonlocality

TL;DR

This paper reveals that quantum nonlocality can be polygamous beyond three observers, challenging the traditional monogamy principle, and demonstrates this with systematic methods and experimental verification using six-photon states.

Contribution

It introduces a systematic approach to identify quantum states and inequalities that violate Bell monogamy beyond three observers, showing the polygamous nature of quantum nonlocality.

Findings

Bell monogamy does not hold universally for more than three observers

Identified inequalities enable multiple observers to simultaneously reveal nonlocality

Experimental verification with six-photon Dicke states confirms the polygamous nature

Abstract

Quantum mechanics imposes limits on the statistics of certain observables. Perhaps the most famous example is the uncertainty principle. Similar trade-offs also exist for the simultaneous violation of multiple Bell inequalities. In the simplest case of three observers, it has been shown that if two observers violate a Bell inequality then none of them can violate any Bell inequality with the third observer, a property called monogamy of Bell violations. Forms of Bell monogamy have been linked to the no-signalling principle and the inability of simultaneous violations of all inequalities is regarded as their fundamental property. Here we show that the Bell monogamy does not hold universally and that in fact the only monogamous situation exists for only three observers. Consequently, the nature of quantum nonlocality is truly polygamous. We present a systematic methodology for identifying quantum states, measurements and tight Bell inequalities that do not obey the monogamy principle for any number of more than three observers. The identified polygamous inequalities enable any subset of $(N-1)$ observers to reveal nonlocality, which is also shown experimentally by measuring Bell-type correlations of six-photon Dicke states. Our findings may be exploited for multiparty quantum key distribution as well as simultaneous self-testing of multiple nodes in quantum networks.