Local unitary invariants of generic multiqubit states

被引：15

作者：

Jing, Naihuan ^{[1
,2
]}

Fei, Shao-Ming ^{[3
,4
]}

Li, Ming ^{[5
]}

Li-Jost, Xianqing ^{[4
]}

Zhang, Tinggui ^{[6
]}

机构：

[1] S China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China

[2] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[3] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

[4] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

[5] China Univ Petr, Dept Math, Qingdao 266555, Shandong, Peoples R China

[6] Hainan Normal Univ, Sch Math & Stat, Haikou 571158, Hainan, Peoples R China

来源：

PHYSICAL REVIEW A | 2015年 / 92卷 / 02期

基金：

中国国家自然科学基金;

关键词：

ENTANGLEMENT; EQUIVALENCE;

D O I：

10.1103/PhysRevA.92.022306

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We present a complete set of local unitary invariants for generic multiqubit systems which gives necessary and sufficient conditions for two states being local unitary equivalent. These invariants are canonical polynomial functions in terms of the generalized Bloch representation of the quantum states. In particular, we prove that there are at most 12 polynomial local unitary invariants for two-qubit states and at most 90 polynomials for three-qubit states. Comparison with Makhlin's 18 local unitary invariants is given for two-qubit systems.

引用

页数：5

共 50 条

[41] Growth of entanglement of generic states under dual-unitary dynamics
Foligno, Alessandro
Bertini, Bruno
PHYSICAL REVIEW B, 2023, 107 (17)
[42] Unitary invariants of qubit systems
Luque, Jean-Gabriel
Thibon, Jean-Yves
Toumazet, Frederic
MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE, 2007, 17 (06) : 1133 - 1151
[43] UNITARY INVARIANTS FOR COMPACT OPERATORS
ARVESON, WB
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 76 (01) : 88 - &
[44] The unitary invariants of a square matrix
Murnaghan, FD
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1932, 18 : 185 - 189
[45] MATRIX INVARIANTS UNITARY AND ORTHOGONAL
SIBIRSKI.KS
DOKLADY AKADEMII NAUK SSSR, 1967, 172 (01): : 40 - &
[46] Entanglement and perfect discrimination of a class of multiqubit states by local operations and classical communication
Bandyopadhyay, Somshubhro
PHYSICAL REVIEW A, 2010, 81 (02):
[47] Local unitary versus local Clifford equivalence of stabilizer and graph states
Zeng, Bei
Chung, Hyeyoun
Cross, Andrew W.
Chuang, Isaac L.
PHYSICAL REVIEW A, 2007, 75 (03):
[48] Graph states and local unitary transformations beyond local Clifford operations
Tsimakuridze, Nikoloz
Guehne, Otfried
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2017, 50 (19)
[49] Invariants of generic immersions
Ekholm, T
PACIFIC JOURNAL OF MATHEMATICS, 2001, 199 (02) : 321 - 345
[50] Symmetric states: Local unitary equivalence via stabilizers
Cenci, Curt D.
Lyons, David W.
Snyder, Laura M.
Walck, Scott N.
Quantum Information and Computation, 2010, 10 (11-12): : 1029 - 1041

← 1 2 3 4 5 →