中国物理B ›› 2018, Vol. 27 ›› Issue (10): 100311-100311.doi: 10.1088/1674-1056/27/10/100311
• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇 下一篇
The stabilizer for n-qubit symmetric states
Xian Shi(石现)
- 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
The stabilizer for n-qubit symmetric states
Xian Shi(石现)1,2,3
- 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
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∈ GL(2,C) such that|φ>=g|φ>. Recently, Gour et al.[Gour G, Kraus B and Wallach N R 2017 J. Math. Phys. 58 092204] presented that almost all n-qubit states|Ψ〉 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|Ψ> 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|φ> 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.
中图分类号: (Entanglement measures, witnesses, and other characterizations)
- 03.67.Mn