Entanglement entropy of multipartite pure states
Abstract
Consider a system consisting of n ddimensional quantum particles and an arbitrary pure state Ψ> of the whole system. Suppose we simultaneously perform complete von Neumann measurements on each particle. The Shannon entropy of the outcomes’ joint probability distribution is a functional of the state Ψ> and of n measurements chosen for each particle. Denote S[Ψ] the minimum of this entropy over all choices of the measurements. We show that S[Ψ] coincides with the entropy of entanglement for bipartite states. We compute S[Ψ] for some special multipartite states: the hexacode state H> (n=6, d=2) and the determinant states Det_{n}> (d=n). The computation yields S[H]=4 log 2 and S[Det_{n}]=log(n!). Counterparts of the determinant state defined for d<n are also considered.
 Publication:

Physical Review A
 Pub Date:
 January 2003
 DOI:
 10.1103/PhysRevA.67.012313
 arXiv:
 arXiv:quantph/0205021
 Bibcode:
 2003PhRvA..67a2313B
 Keywords:

 03.67.a;
 03.65.w;
 Quantum information;
 Quantum mechanics;
 Quantum Physics
 EPrint:
 7 pages, REVTeX, corrected some typos