2010/05/25 by Michael M. Wolf, Wolf, Michael M., David Pérez García +1 · 2 citations
Computer Science · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.1005.4545
openalex publication_date 2010/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.