Entanglement entropy of multipartite pure states

Abstract

Consider a system consisting of $n$ $d$-dimensional quantum particles and arbitrary pure state $\Psi$ of the whole system. Suppose we simultaneously perform complete von Neumann measurements on each particle. One can ask: what is the minimal possible value $S[\Psi ]$ of the entropy of outcomes joint probability distribution? We show that $S[\Psi ]$ coincides with entanglement entropy for bipartite states. We compute $S[\Psi ]$ for two sample multipartite states: the hexacode state ($n=6,d=2$) and determinant states ($n=d$). The generalization of determinant states to the case $d<n$ is considered.

7 pages, REVTeX, corrected some typos

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