Construction of quantum states with special properties by projection methods

被引：1

作者：

Duan, Xuefeng ^{[1
]}

Li, Chi-Kwong ^{[2
]}

Pelejo, Diane Christine ^{[3
]}

机构：

[1] Guilin Univ Elect Technol, Coll Math & Computat Sci, Guilin 541004, Peoples R China

[2] Coll William & Mary, Dept Math, Williamsburg, VA 23185 USA

[3] Univ Philippines Diliman, Coll Sci, Inst Math, Quezon City 1101, Philippines

来源：

QUANTUM INFORMATION PROCESSING | 2020年 / 19卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Quantum states; Reduced  (marginal)  states; Tensor product; Positive semidefinite matrices; Density matrices; Projections; GRADIENT METHODS; CONVERGENCE; EIGENVALUES;

D O I：

10.1007/s11128-020-02881-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We use projection methods to construct (global) quantum states with prescribed reduced (marginal) states, and possibly with some special properties such as having specific eigenvalues, having specific rank and extreme von Neumann or Renyi entropy. Using convex analysis, optimization techniques on matrix manifolds, we obtain algorithms to solve the problem. MATLAB programs are written based on these algorithms, and numerical examples are illustrated. The numerical results reveal new patterns leading to new insights and research problems on the topic.

引用

页数：34

共 22 条

[1] Nonmonotone spectral projected gradient methods on convex sets [J].

Birgin, EG ;

Martínez, JM ;

Raydan, M .

SIAM JOURNAL ON OPTIMIZATION, 2000, 10 (04) :1196-1211

[2] Inexact spectral projected gradient methods on convex sets [J].

Birgin, EG ;

Martínez, JM ;

Raydan, M .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2003, 23 (04) :539-559

[3]

Boyle J.P., 1986, LECT NOTES STAT, V37

[4] Detecting consistency of overlapping quantum marginals by separability [J].

Chen, Jianxin ;

Ji, Zhengfeng ;

Yu, Nengkun ;

Zeng, Bei .

PHYSICAL REVIEW A, 2016, 93 (03)

[5] Quantum state transformations and the Schubert calculus [J].

Daftuar, S ;

Hayden, P .

ANNALS OF PHYSICS, 2005, 315 (01) :80-122

[6]

Douglas J., 1956, T AM MATH SOC, V82, P421, DOI [DOI 10.1090/S0002-9947-1956-0084194-4, DOI 10.2307/1993056]

[7] Eigenvalues, invariant factors, highest weights, and Schubert calculus [J].

Fulton, W .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 37 (03) :209-249

[8]

GOLUB GH, 1973, SIAM REV, V15, P318, DOI 10.1137/1015032

[9] COMPUTING A NEAREST SYMMETRIC POSITIVE SEMIDEFINITE MATRIX [J].

HIGHAM, NJ .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1988, 103 :103-118

[10] Rank two bipartite bound entangled states do not exist [J].

Horodecki, P ;

Smolin, JA ;

Terhal, BM ;

Thapliyal, AV .

THEORETICAL COMPUTER SCIENCE, 2003, 292 (03) :589-596

← 1 2 3 →