Witnessing Bell violations through probabilistic negativity

Abstract

Bell's theorem shows that no hidden-variable model can explain the measurement statistics of a quantum system shared between two parties, thus ruling out a classical (local) understanding of nature. In this work we demonstrate that by relaxing the positivity restriction in the hidden-variable probability distribution it is possible to derive quasiprobabilistic Bell inequalities whose sharp upper bound is written in terms of a negativity witness of said distribution. This provides an analytic solution for the amount of negativity necessary to violate the CHSH inequality by an arbitrary amount, therefore revealing the amount of negativity required to emulate the quantum statistics in a Bell test.

Anomalous weak values require coherence

“…The idea of studying anomalous weak values from the perspective of anomalous quasi-probabilities has also appeared before in a less general description. From a rather broad view, negative joint quasi-probabilities are always capable of reproducing experimental data in quantum theory [27,28], but there are many such distributions capable of reproducing the strongest possible quantum correlations [29][30][31][32], a fact that somewhat disfavours those as good explanations due to fine-tuning arguments. Ref.…”