Homology of Generic Stabilizer States

Details Homology of Generic Stabilizer States Homology of Generic Stabilizer States

2008-09-19

arxiv.org/abs/0809.3346v1

Physics

Quantum Physics

14 pages

Scientific paper

This work is concerned with multi-party stabilizer states in the sense of quantum information theory. We investigate the homological invariants for states of which each party holds a large equal number N of quantum bits. We show that in many cases there is a generic expected value of the invariants: for large N it is approximated with arbitrarily high probability if a stabilizer state is chosen at random. The result suggests that typical entanglement of stabilizer states involves but the sets comprising just over one half of the parties. Our main tool is the Bruhat decomposition from the theory of finite Chevalley groups.

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