Eberhard limit for photon-counting Bell tests and its utility in quantum key distribution

TL;DR

This paper extends Eberhard's limit to photon-counting Bell tests, demonstrating their universality for multiphoton states and improving quantum key distribution by increasing loss tolerance and key rates.

Contribution

It shows that the Eberhard limit applies to photon-counting Bell tests for multiphoton states and introduces photon-counting CGLMP inequalities matching this limit.

Findings

Eberhard limit holds for photon-counting CHSH Bell tests with multiphoton states

Photon-counting CGLMP inequalities can also reach the Eberhard limit

Enhanced loss tolerance improves QKD key rates and security

Abstract

Loophole-free Bell tests are essential if one wishes to perform device-independent quantum key distribution (QKD), since any loophole could be used by a potential adversary to undermine the security of the protocol. Crucial work by Eberhard demonstrated that weakly entangled two-qubit states have a far greater resistance to the detection loophole than maximally entangled states, allowing one to close the loophole with detection efficiency greater than 2/3. Here we demonstrate that this same limit holds for photon-counting CHSH Bell tests which can demonstrate non-locality for higher dimensional multiphoton states such as two-mode squeezed vacuum and generalized Holland-Burnett states. In fact, we show evidence that these tests are in some sense universal, allowing feasible detection loophole-free tests for any multiphoton bipartite state, as long as the two modes are well correlated in photon number. Additionally, by going beyond the typical two-input two-output Bell scenario, we show that there are also photon-counting CGLMP inequalities which can also match the Eberhard limit, paving the way for more exotic loophole-free Bell tests. Finally we show that by exploiting this increased loss tolerance of non maximally entangled states, one can increase the key rates and loss tolerances of QKD protocols based on photon-counting tests.