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.
Asymptotic Entanglement Hiding under Stabilizer Restrictions
School of Computer Science and Technology, University of Science and Technology of China（中国科学技术大学计算机科学与技术学院）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；School of Software Engineering, University of Science and Technology of China（中国科学技术大学软件工程学院）；Suzhou Institute for Advanced Research, University of Science and Technology of China（中国科学技术大学苏州高等研究院）
$N$-Party Hadamard Test for Distributed Quantum Computation
NTT Computer and Data Science Laboratories, NTT Corporation（NTT 计算机与数据科学实验室）；Department of Electrical, Electronic, and Communication Engineering, Faculty of Science and Engineering, Chuo University（中央大学理工学部电气电子通信工程系）；JST, PRESTO（日本科学技术振兴机构 PRESTO 项目）
Tata Institute of Fundamental Research（塔塔基础研究所）；National Tsing Hua University（国立清华大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
Entirely nonlocal quantum magic without entanglement
Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）；Beijing Key Laboratory of Fault-Tolerant Quantum Computing, Beijing Academy of Quantum Information Sciences（北京容错量子计算北京市重点实验室，北京量子信息科学研究院）
