Loss tolerance under alternative multipartite Bell inequalities

Determine whether the loss-tolerance advantage of the vacuum–n-photon encoding persists for other multipartite Bell inequalities and whether alternative inequalities provide more favourable scaling with the number of parties.

Background

The paper establishes that, for parity–CHSH tests, the vacuum–n-photon GHZ encoding has a lower critical detection-efficiency threshold than the fixed-photon-number encoding for every even number of parties. This advantage arises from the encoding-dependent behaviour of diagonal correlations under photon loss, rather than from improved preservation of off-diagonal coherence.

The authors identify as future work the question of whether this loss-tolerance benefit is specific to the parity–CHSH functional or extends to other multipartite Bell inequalities. They also leave unresolved whether another inequality could yield more favourable dependence of the detection-efficiency threshold on the number of parties, which is important for scaling device-independent conference key agreement and related multipartite quantum-network applications.