RT Journal Article
T1 The inverse eigenvalue problem for quantum channels
A1 Wolf, Michael
A1 Pérez García, David
AB 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.
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/41898
UL https://hdl.handle.net/20.500.14352/41898
LA eng
NO Unión Europea. FP7
NO Comunidad de Madrid
NO Danish research council (FNU)
DS Docta Complutense
RD 11 may 2025