Quantum correlations and N-representability

Antonio Acin

ICFO-The Institute of Photonic Sciences

Abstract

We consider two apparently disconnected problems: (i) characterize the correlations that are possible among different quantum systems and (ii) find the conditions for N-representability. We show that these problems, among many others, can be tackled by a convergent hierarchy of semi-definite programs. This hierarchy can be understood as the generalization to the non-commutative case of well-known classical optimization methods by Lasserre and Parrilo. We conclude by discussing the application of this method to other relevant quantum scenarios.