The geometric measure of entanglement for symmetric states

Details The geometric measure of entanglement for symmetric states The geometric measure of entanglement for symmetric states

2009-05-29

arxiv.org/abs/0905.4822v2

Phys. Rev. A 80, 032324 (2009)

Physics

Quantum Physics

V2: significantly extended, 6 pages, no figures

Scientific paper

10.1103/PhysRevA.80.032324

Is the closest product state to a symmetric entangled multiparticle state also symmetric? This question has appeared in the recent literature concerning the geometric measure of entanglement. First, we show that a positive answer can be derived from results concerning symmetric multilinear forms and homogeneous polynomials, implying that the closest product state can be chosen to be symmetric. We then prove the stronger result that the closest product state to any symmetric multiparticle quantum state is necessarily symmetric. Moreover, we discuss generalizations of our result and the case of translationally invariant states, which can occur in spin models.

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