Abstract
Verifying entanglement between parties is essential for creating a secure quantum network, and Bell tests are the most rigorous method for doing so. However, if there is any signalling between the parties, then the violation of these inequalities can no longer be used to draw conclusions about the presence of entanglement. There is a pressing need to examine the role of signalling in quantum communication protocols from multiple perspectives, including communication security, physics foundations, and resource utilization while also promoting innovative technological applications. Here, we propose a semi-device independent protocol that allows us to numerically correct for effects of correlations in experimental probability distributions, caused by statistical fluctuations and experimental imperfections. Our noise robust protocol presents a relaxation of a tomography-based optimisation method called the steering robustness. The proposed protocol is numerically and experimentally analyzed in the context of random, misaligned measurements, correcting for signalling where necessary, resulting in a higher probability of violation compared to existing state-of-the-art inequalities. Our work demonstrates the power of semidefinite programming for entanglement verification and brings quantum networks closer to practical applications.
