Separable state

Summary

A separable state of a two-part quantum system is a mixture of product states. Two parties can prepare it with local operations and shared classical randomness. The separable states form a closed convex set inside the set of all density matrices. A state that is not separable is entangled. Deciding whether a given state is separable is a central problem; the Peres–Horodecki criterion solves it in small dimensions.