Tests of multimode quantum non-locality with homodyne measurements

TL;DR

This paper demonstrates that using multimode continuous-variable states with homodyne measurements can exponentially increase Bell inequality violations, potentially enabling loophole-free tests that are robust to noise and experimental imperfections.

Contribution

It proves exponential growth in Bell violation with the number of modes using homodyne measurements and analyzes practical advantages for multipartite Bell tests.

Findings

Bell violation grows exponentially with modes

Maximum quantum violation achievable for any number of modes

Enhanced noise robustness with more modes

Abstract

We investigate the violation of local realism in Bell tests involving homodyne measurements performed on multimode continuous-variable states. By binning the measurement outcomes in an appropriate way, we prove that the Mermin-Klyshko inequality can be violated by an amount that grows exponentially with the number of modes. Furthermore, the maximum violation allowed by quantum mechanics can be attained for any number of modes, albeit requiring a quantum state that is rather unrealistic. Interestingly, this exponential increase of the violation holds true even for simpler states, such as multipartite GHZ states. The resulting benefit of using more modes is shown to be significant in practical multipartite Bell tests by analyzing the increase of the robustness to noise with the number of modes. In view of the high efficiency achievable with homodyne detection, our results thus open a possible way to feasible loophole-free Bell tests that are robust to experimental imperfections. We provide an explicit example of a three-mode state (a superposition of coherent states) which results in a significantly high violation of the Mermin-Klyshko inequality (around 10%) with homodyne measurements.