# Protocol and quantum circuits for realizing deterministic entanglement concentration

## Abstract

Entanglement concentration can be achieved in a deterministic fashion [Morikoshi, Phys. Rev. Lett. 84, 3189 (2000); Phys. Rev. A 64, 022316 (2001)]. We present a protocol for deterministic extraction of an Einstein-Podolsky-Rosen pair from two partially entangled pairs via local operations and classical communication. This protocol consists of a generalized measurement described by a positive operator-valued measure (POVM), one-way classical communication, and a corresponding unitary operation or a choice between the two pairs. Based on the theory of majorization, we explicitly construct the required POVM, which can be realized by performing a unitary operation in the extended space and a conventional Von Neuman orthogonal measurement. By decomposing the evolution process from the initial state to the final state, we construct the quantum circuits for realizing the unitary operation with quantum Toffoli gates, and thus provide a physical means to realize the deterministic entanglement concentration. Our method for constructing quantum circuits differs from the usual method based on decomposition of unitary matrices, and is convenient for a large class of quantum processes involving generalized measurements.

- Authors:

- Department of Physics, Ocean University of China, Qingdao 266071 (China)
- Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026 (China)

- Publication Date:

- OSTI Identifier:
- 20974537

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.73.022321; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMMUNICATIONS; DIGITAL CIRCUITS; INFORMATION THEORY; MATRICES; PARAMAGNETISM; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS

### Citation Formats

```
Gu Yongjian, Li Wendong, and Guo Guangcan.
```*Protocol and quantum circuits for realizing deterministic entanglement concentration*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.022321.

```
Gu Yongjian, Li Wendong, & Guo Guangcan.
```*Protocol and quantum circuits for realizing deterministic entanglement concentration*. United States. doi:10.1103/PHYSREVA.73.022321.

```
Gu Yongjian, Li Wendong, and Guo Guangcan. Wed .
"Protocol and quantum circuits for realizing deterministic entanglement concentration". United States.
doi:10.1103/PHYSREVA.73.022321.
```

```
@article{osti_20974537,
```

title = {Protocol and quantum circuits for realizing deterministic entanglement concentration},

author = {Gu Yongjian and Li Wendong and Guo Guangcan},

abstractNote = {Entanglement concentration can be achieved in a deterministic fashion [Morikoshi, Phys. Rev. Lett. 84, 3189 (2000); Phys. Rev. A 64, 022316 (2001)]. We present a protocol for deterministic extraction of an Einstein-Podolsky-Rosen pair from two partially entangled pairs via local operations and classical communication. This protocol consists of a generalized measurement described by a positive operator-valued measure (POVM), one-way classical communication, and a corresponding unitary operation or a choice between the two pairs. Based on the theory of majorization, we explicitly construct the required POVM, which can be realized by performing a unitary operation in the extended space and a conventional Von Neuman orthogonal measurement. By decomposing the evolution process from the initial state to the final state, we construct the quantum circuits for realizing the unitary operation with quantum Toffoli gates, and thus provide a physical means to realize the deterministic entanglement concentration. Our method for constructing quantum circuits differs from the usual method based on decomposition of unitary matrices, and is convenient for a large class of quantum processes involving generalized measurements.},

doi = {10.1103/PHYSREVA.73.022321},

journal = {Physical Review. A},

number = 2,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}