# Local unitary equivalence of quantum states and simultaneous orthogonal equivalence

## Abstract

The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through simultaneous similarity under projective orthogonal transformations, and four parametrization independent algorithms are proposed to judge when two density matrices on ℂ{sup d{sub 1}} ⊗ ℂ{sup d{sub 2}} are locally unitary equivalent in connection with trace identities, Kronecker pencils, Albert determinants and Smith normal forms.

- Authors:

- Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695 (United States)
- College of Applied Science, Beijing University of Technology, Beijing 100124 (China)

- Publication Date:

- OSTI Identifier:
- 22596847

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; DENSITY MATRIX; ORTHOGONAL TRANSFORMATIONS; QUANTUM STATES

### Citation Formats

```
Jing, Naihuan, E-mail: jing@ncsu.edu, Yang, Min, and Zhao, Hui, E-mail: zhaohui@bjut.edu.cn.
```*Local unitary equivalence of quantum states and simultaneous orthogonal equivalence*. United States: N. p., 2016.
Web. doi:10.1063/1.4954230.

```
Jing, Naihuan, E-mail: jing@ncsu.edu, Yang, Min, & Zhao, Hui, E-mail: zhaohui@bjut.edu.cn.
```*Local unitary equivalence of quantum states and simultaneous orthogonal equivalence*. United States. doi:10.1063/1.4954230.

```
Jing, Naihuan, E-mail: jing@ncsu.edu, Yang, Min, and Zhao, Hui, E-mail: zhaohui@bjut.edu.cn. Wed .
"Local unitary equivalence of quantum states and simultaneous orthogonal equivalence". United States.
doi:10.1063/1.4954230.
```

```
@article{osti_22596847,
```

title = {Local unitary equivalence of quantum states and simultaneous orthogonal equivalence},

author = {Jing, Naihuan, E-mail: jing@ncsu.edu and Yang, Min and Zhao, Hui, E-mail: zhaohui@bjut.edu.cn},

abstractNote = {The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through simultaneous similarity under projective orthogonal transformations, and four parametrization independent algorithms are proposed to judge when two density matrices on ℂ{sup d{sub 1}} ⊗ ℂ{sup d{sub 2}} are locally unitary equivalent in connection with trace identities, Kronecker pencils, Albert determinants and Smith normal forms.},

doi = {10.1063/1.4954230},

journal = {Journal of Mathematical Physics},

number = 6,

volume = 57,

place = {United States},

year = {Wed Jun 15 00:00:00 EDT 2016},

month = {Wed Jun 15 00:00:00 EDT 2016}

}

DOI: 10.1063/1.4954230

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