# Measurement-driven quantum evolution

## Abstract

We study the problem of mapping an unknown mixed quantum state onto a known pure state without the use of unitary transformations. This is achieved with the help of sequential measurements of two noncommuting observables only. We show that the overall success probability is maximized in the case of measuring two observables whose eigenstates define mutually unbiased bases. We find that for this optimal case the success probability quickly converges to unity as the number of measurement processes increases and that it is almost independent of the initial state. In particular, we show that to guarantee a success probability close to one the number of consecutive measurements must be larger than the dimension of the Hilbert space. We connect these results to quantum copying, quantum deleting, and entanglement generation.

- Authors:

- Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)
- (Chile)
- (Mexico)

- Publication Date:

- OSTI Identifier:
- 20786667

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.73.012322; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; EIGENSTATES; ENERGY LEVELS; EVOLUTION; HILBERT SPACE; MAPPING; PROBABILITY; QUANTUM ENTANGLEMENT; TRANSFORMATIONS; UNITARITY

### Citation Formats

```
Roa, L., Delgado, A., Ladron de Guevara, M. L., Klimov, A. B., Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta, Chile and Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion, and Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco.
```*Measurement-driven quantum evolution*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.

```
Roa, L., Delgado, A., Ladron de Guevara, M. L., Klimov, A. B., Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta, Chile and Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion, & Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco.
```*Measurement-driven quantum evolution*. United States. doi:10.1103/PHYSREVA.73.0.

```
Roa, L., Delgado, A., Ladron de Guevara, M. L., Klimov, A. B., Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta, Chile and Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion, and Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco. Sun .
"Measurement-driven quantum evolution". United States.
doi:10.1103/PHYSREVA.73.0.
```

```
@article{osti_20786667,
```

title = {Measurement-driven quantum evolution},

author = {Roa, L. and Delgado, A. and Ladron de Guevara, M. L. and Klimov, A. B. and Departamento de Fisica, Universidad Catolica del Norte, Casilla 1280, Antofagasta, Chile and Center for Quantum Optics and Quantum Information, Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion and Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco},

abstractNote = {We study the problem of mapping an unknown mixed quantum state onto a known pure state without the use of unitary transformations. This is achieved with the help of sequential measurements of two noncommuting observables only. We show that the overall success probability is maximized in the case of measuring two observables whose eigenstates define mutually unbiased bases. We find that for this optimal case the success probability quickly converges to unity as the number of measurement processes increases and that it is almost independent of the initial state. In particular, we show that to guarantee a success probability close to one the number of consecutive measurements must be larger than the dimension of the Hilbert space. We connect these results to quantum copying, quantum deleting, and entanglement generation.},

doi = {10.1103/PHYSREVA.73.0},

journal = {Physical Review. A},

number = 1,

volume = 73,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}