Concurrence vectors of multipartite states based on coefficient matrices

Abstract

In this paper, we propose a concurrence vector for a multipartite qudit pure state based on its coefficient matrices and define its norm as the generalized concurrence. Moreover, we prove that this generalized concurrence is a good measure according to the three necessary conditions that any measure of entanglement has to satisfy, i.e. it equals zero if and only if the state is separable, it remains invariant under local unitary transformations, and it is not increasing under local operations and classical communication. This generalized concurrence is very practical and convenient for computation.