Quantum Nonlocality and Inseparability

Abstract

A quantum system consisting of two subsystems is separable if its density matrix can be written as $\rho = \sum {{w_K}} {\mkern 1mu} {\rho '_K} \otimes {\rho ''_K}$ where ${\rho '_K}$ and ${\rho ''_K}$ are density matrices for the two subsytems, and the positive weights w ^k satisfy $\sum {{w_K}} = 1.$ A necessary condition for separability is derived and is shown to be more sensitive than Bell’s inequality for detecting quantum inseparability. Moreover, collective tests of Bell’s inequality (namely, tests that involve several composite systems simultaneously) may sometimes lead to a violation of Bell’s inequality, even if the latter is satisfied when each composite system is tested separately.