The stabilizer for..-qubit symmetric states

查看全文 作　　者：[1,2,3]石现 机构地区：[1]Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;[2]University of Chinese Academy of Sciences, Beijing 100049, China;[3]UTS-AMSS Joint Research Laboratory for Quantum Computation and Quantum Information Processing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 出　　处：《Chinese Physics B》索引2018年第27卷第10期,共8页 基　　金：Project partially supported by the National Key Research and Development Program of China(Grant No.2016YFB1000902);the National Natural Science Foundation of China(Grant Nos.61232015 and 61621003);the Knowledge Innovation Program of the Chinese Academy of Sciences(CAS);Institute of Computing Technology of CAS 摘　　要：The stabilizer group for an n-qubit state |Φ> is the set of all invertible local operators(ILO) g = g1g2···gn,gi 2 GL(2,C) such that |Φ>= g|Φ>. Recently, Gour et al. [Gour G, Kraus B and Wallach N R 2017 J. Math. Phys. 58092204] presented that almost all n-qubit states jyi own a trivial stabilizer group when n≥5. In this article, we consider the case when the stabilizer group of an n-qubit symmetric pure state jyi is trivial. First we show that the stabilizer group for an n-qubit symmetric pure state |Φ> is nontrivial when n≤4. Then we present a class of n-qubit symmetric states |Ψ> with a trivial stabilizer group when n≥5. Finally, we propose a conjecture and prove that an n-qubit symmetric pure state owns a trivial stabilizer group when its diversity number is bigger than 5 under the conjecture we make, which confirms the main result of Gour et al. partly. 关 键 词：状态 对称 操作员 证明