Quantifying entanglement with probabilities

Abstract

We propose a new approach to the problem of defining the degree of entanglement between two particles in a pure state with Hilbert spaces of arbitrary finite dimensions. The central idea is that entanglement gives rise to correlations between the particles that do not occur in separable states. We individuate the contributions of these correlations to the joint and the conditional probabilities of local measurements outcomes. We use these probabilities to define the measure of entanglement. Our measure turns out to be proportional to the so-called 2-entropy and therefore satisfies the properties required for any measure of entanglement. We conclude with an outlook on the problem of extending our approach to the case of multipartite systems and mixed states.