# Conclusive discrimination among N equidistant pure states

## Abstract

We find the allowed complex overlaps for N equidistant pure quantum states. The accessible overlaps define a petal-shaped area on the Argand plane. Each point inside the petal represents a set of N linearly independent pure states and each point on its contour represents a set of N linearly dependent pure states. We find the optimal probabilities of success of discriminating unambiguously in which of the N equidistant states the system is. We show that the phase of the involved overlap plays an important role in the probability of success. For a fixed overlap modulus, the success probability is highest for the set of states with an overlap with phase equal to zero. In this case, if the process fails, then the information about the prepared state is lost. For states with a phase different from zero, the information could be obtained with an error-minimizing measurement protocol.

- Authors:

- Departamento de Fisica, Universidad de Concepcion, Barrio Universitario, Casilla 160-C, Concepcion (Chile)
- Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico)

- Publication Date:

- OSTI Identifier:
- 22058799

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; PROBABILITY; PURE STATES; QUANTUM INFORMATION

### Citation Formats

```
Roa, Luis, Hermann-Avigliano, Carla, Salazar, R., and Klimov, A. B..
```*Conclusive discrimination among N equidistant pure states*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.014302.

```
Roa, Luis, Hermann-Avigliano, Carla, Salazar, R., & Klimov, A. B..
```*Conclusive discrimination among N equidistant pure states*. United States. doi:10.1103/PHYSREVA.84.014302.

```
Roa, Luis, Hermann-Avigliano, Carla, Salazar, R., and Klimov, A. B.. Fri .
"Conclusive discrimination among N equidistant pure states". United States. doi:10.1103/PHYSREVA.84.014302.
```

```
@article{osti_22058799,
```

title = {Conclusive discrimination among N equidistant pure states},

author = {Roa, Luis and Hermann-Avigliano, Carla and Salazar, R. and Klimov, A. B.},

abstractNote = {We find the allowed complex overlaps for N equidistant pure quantum states. The accessible overlaps define a petal-shaped area on the Argand plane. Each point inside the petal represents a set of N linearly independent pure states and each point on its contour represents a set of N linearly dependent pure states. We find the optimal probabilities of success of discriminating unambiguously in which of the N equidistant states the system is. We show that the phase of the involved overlap plays an important role in the probability of success. For a fixed overlap modulus, the success probability is highest for the set of states with an overlap with phase equal to zero. In this case, if the process fails, then the information about the prepared state is lost. For states with a phase different from zero, the information could be obtained with an error-minimizing measurement protocol.},

doi = {10.1103/PHYSREVA.84.014302},

journal = {Physical Review. A},

issn = {1050-2947},

number = 1,

volume = 84,

place = {United States},

year = {2011},

month = {7}

}