Matrix permanent and quantum entanglement of permutation invariant states

Tzu-Chieh Wei, Simone Severini

Published 2009-04-30, updated 2010-11-06Version 2

We point out that a geometric measure of quantum entanglement is related to the matrix permanent when restricted to permutation invariant states. This connection allows us to interpret the permanent as an angle between vectors. By employing a recently introduced permanent inequality by Carlen, Loss and Lieb, we can prove explicit formulas of the geometric measure for permutation invariant basis states in a simple way.