English

Standard forms of noisy quantum operations via depolarization

Quantum Physics 2009-11-11 v1

Abstract

We consider noisy, non-local unitary operations or interactions, i.e. the corresponding evolutions are described by completely positive maps or master equations of Lindblad form. We show that by random local 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 ideal unitary operation is given by some 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.

Keywords

Cite

@article{arxiv.quant-ph/0507134,
  title  = {Standard forms of noisy quantum operations via depolarization},
  author = {W. Dür and M. Hein and J. I. Cirac and H. -J. Briegel},
  journal= {arXiv preprint arXiv:quant-ph/0507134},
  year   = {2009}
}

Comments

29 pages, 4 figures

R2 v1 2026-07-22T19:49:54.753Z