2008/09/19 by Klaus Wirthmüller, Wirthmüller, Klaus
Computer Science · Mathematics · #Algebraic structures and combinatorial models #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.0809.3346
openalex publication_date 2008/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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.