# Optimal time reversal of multiphase equatorial states

## Abstract

Even though the time reversal is unphysical (it corresponds to the complex conjugation of the density matrix), for some restricted set of states it can be achieved unitarily, typically when there is a common dephasing in a n-level system. However, in the presence of multiple phases (i.e., a different dephasing for each element of an orthogonal basis occurs) the time reversal is no longer physically possible. In this paper we derive the channel which optimally approaches in fidelity the time reversal of multiphase equatorial states in arbitrary (finite) dimension. We show that, in contrast to the customary case of the universal-NOT on qubits (or the universal conjugation in arbitrary dimension), the optimal phase covariant time reversal for equatorial states is a nonclassical channel, which cannot be achieved via a measurement-and-preparation procedure. Unitary realizations of the optimal time reversal channel are given with minimal ancillary dimension, exploiting the simplex structure of the optimal maps.

- Authors:

- QUIT Group, Dipartimento di Fisica 'A. Volta', Universita di Pavia, via Bassi 6, I-27100 Pavia (Italy)

- Publication Date:

- OSTI Identifier:
- 20786274

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.062311; (c) 2005 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; DENSITY MATRIX; ENERGY LEVELS; INFORMATION THEORY; LOGIC CIRCUITS; QUANTUM COMPUTERS; QUANTUM MECHANICS; QUBITS

### Citation Formats

```
Buscemi, Francesco, D'Ariano, Giacomo Mauro, and Macchiavello, Chiara.
```*Optimal time reversal of multiphase equatorial states*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Buscemi, Francesco, D'Ariano, Giacomo Mauro, & Macchiavello, Chiara.
```*Optimal time reversal of multiphase equatorial states*. United States. doi:10.1103/PHYSREVA.72.0.

```
Buscemi, Francesco, D'Ariano, Giacomo Mauro, and Macchiavello, Chiara. Thu .
"Optimal time reversal of multiphase equatorial states". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786274,
```

title = {Optimal time reversal of multiphase equatorial states},

author = {Buscemi, Francesco and D'Ariano, Giacomo Mauro and Macchiavello, Chiara},

abstractNote = {Even though the time reversal is unphysical (it corresponds to the complex conjugation of the density matrix), for some restricted set of states it can be achieved unitarily, typically when there is a common dephasing in a n-level system. However, in the presence of multiple phases (i.e., a different dephasing for each element of an orthogonal basis occurs) the time reversal is no longer physically possible. In this paper we derive the channel which optimally approaches in fidelity the time reversal of multiphase equatorial states in arbitrary (finite) dimension. We show that, in contrast to the customary case of the universal-NOT on qubits (or the universal conjugation in arbitrary dimension), the optimal phase covariant time reversal for equatorial states is a nonclassical channel, which cannot be achieved via a measurement-and-preparation procedure. Unitary realizations of the optimal time reversal channel are given with minimal ancillary dimension, exploiting the simplex structure of the optimal maps.},

doi = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 6,

volume = 72,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}