A Markovian Model for Joint Observations, Bell's Inequality and Hidden States

Abstract

While the standard approach to quantum systems studies length preserving linear transformations of wave functions, the Markov picture focuses on trace preserving operators on the space of Hermitian (self-adjoint) matrices. The Markov approach extends the standard one and provides a refined analysis of measurements and quantum Markov chains. In particular, Bell's inequality becomes structurally clear. It turns out that hidden state models are natural in the Markov context. In particular, a violation of Bell's inequality is seen to be compatible with the existence of hidden states. The Markov model moreover clarifies the role of the "negative probabilities" in Feynman's analysis of the EPR paradox.