Wolf, Michael and Pérez García, David
(2010)
*The inverse eigenvalue problem for quantum channels.*
(Submitted)

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Official URL: http://arxiv.org/abs/1005.4545

## Abstract

Given a list of n complex numbers, when can it be the spectrum of a quantum channel, i.e., a completely positive trace preserving map? We provide an explicit solution for the n=4 case and show that in general the characterization of the non-zero part of the spectrum can essentially be given in terms of its classical counterpart - the non-zero spectrum of a stochastic matrix. A detailed comparison between the classical and quantum case is given. We discuss applications of our findings in the analysis of time-series and correlation functions and provide a general characterization of the peripheral spectrum, i.e., the set of eigenvalues of modulus one. We show that while the peripheral eigen-system has the same structure for all Schwarz maps, the constraints imposed on the rest of the spectrum change immediately if one departs from complete positivity.

Item Type: | Article |
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Uncontrolled Keywords: | Física matemática, Teoría cuántica, Teoría espectral, Quantum Physics, Mathematical Physics, Spectral Theory |

Subjects: | Sciences > Physics > Mathematical physics Sciences > Physics > Quantum theory |

ID Code: | 12156 |

Deposited On: | 03 Feb 2011 08:33 |

Last Modified: | 04 Dec 2014 10:26 |

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