  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.
