# Standard forms of noisy quantum operations via depolarization

## Abstract

We consider completely positive maps that describe noisy, multiparticle unitary operations. We show that by random single-particle operations the completely positive maps can be depolarized to a standard form with a reduced number of parameters describing the noise process in such a way that the noiseless (unitary) part of the evolution is not altered. A further reduction of the parameters, in many cases even to a single one (i.e., global white noise), is possible by tailoring the decoherence process and increasing the amount of noise. We generalize these results to the dynamical case where the noisy evolution is described by a master equation of Lindblad form, and the noiseless evolution is specified by an interaction Hamiltonian. The resulting standard forms may be used to compute lower bounds on channel capacities, to simplify quantum process tomography or to derive error thresholds for entanglement purification and quantum computation.

- Authors:

- Institut fuer Theoretische Physik, Universitaet Innsbruck, Technikerstrasse 25, A-6020 Innsbruck (Austria)
- (Austria)
- Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching (Germany)

- Publication Date:

- OSTI Identifier:
- 20786478

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052326; (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; CAPACITY; CORRECTIONS; DEPOLARIZATION; ERRORS; HAMILTONIANS; NOISE; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; RANDOMNESS; TOMOGRAPHY

### Citation Formats

```
Duer, W., Briegel, H.-J., Institut fuer Quantenoptik und Quanteninformation der Oesterreichischen Akademie der Wissenschaften, Innsbruck, Hein, M., and Cirac, J. I..
```*Standard forms of noisy quantum operations via depolarization*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Duer, W., Briegel, H.-J., Institut fuer Quantenoptik und Quanteninformation der Oesterreichischen Akademie der Wissenschaften, Innsbruck, Hein, M., & Cirac, J. I..
```*Standard forms of noisy quantum operations via depolarization*. United States. doi:10.1103/PHYSREVA.72.0.

```
Duer, W., Briegel, H.-J., Institut fuer Quantenoptik und Quanteninformation der Oesterreichischen Akademie der Wissenschaften, Innsbruck, Hein, M., and Cirac, J. I.. Tue .
"Standard forms of noisy quantum operations via depolarization". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786478,
```

title = {Standard forms of noisy quantum operations via depolarization},

author = {Duer, W. and Briegel, H.-J. and Institut fuer Quantenoptik und Quanteninformation der Oesterreichischen Akademie der Wissenschaften, Innsbruck and Hein, M. and Cirac, J. I.},

abstractNote = {We consider completely positive maps that describe noisy, multiparticle unitary operations. We show that by random single-particle operations the completely positive maps can be depolarized to a standard form with a reduced number of parameters describing the noise process in such a way that the noiseless (unitary) part of the evolution is not altered. A further reduction of the parameters, in many cases even to a single one (i.e., global white noise), is possible by tailoring the decoherence process and increasing the amount of noise. We generalize these results to the dynamical case where the noisy evolution is described by a master equation of Lindblad form, and the noiseless evolution is specified by an interaction Hamiltonian. The resulting standard forms may be used to compute lower bounds on channel capacities, to simplify quantum process tomography or to derive error thresholds for entanglement purification and quantum computation.},

doi = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 5,

volume = 72,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}