Abstract
A remarkable feature of quantum entanglement is that an entangled state of two parties, Alice ( ) and Bob ( ), may be more disordered locally than globally. That is, , where is the von Neumann entropy. It is known that satisfaction of this inequality implies that a state is nonseparable. In this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system is majorized by the vector of eigenvalues of the density matrix of system alone. This gives a strong sense in which a separable state is more disordered globally than locally and a new necessary condition for separability of bipartite states in arbitrary dimensions.
- Received 29 November 2000
DOI:https://doi.org/10.1103/PhysRevLett.86.5184
©2001 American Physical Society