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QI: Fachverband Quanteninformation

QI 29: Quantum Information: Concepts and Methods I

QI 29.4: Vortrag

Donnerstag, 13. März 2025, 12:00–12:15, HS IV

Channels and Dynamics Are Almost Always Diagonalizable — •Frederik vom Ende — Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany

While the Choi matrix of a quantum channel can always be diagonalized—even unitarily—it remains a surprisingly common misconception that the same is true for the channel itself (or, equivalently, for its representation matrix in the standard basis). To clarify this, we provide simple examples of channels that exhibit non-trivial Jordan blocks. The main contribution of this work then is a proof of the statement: “The collection of all elements of S that have only simple eigenvalues is dense in S” for various sets S, including: all quantum channels, unital channels, positive trace-preserving maps, Lindbladians (GKSL-generators), and time-dependent Markovian channels. In particular, this result demonstrates that any element from each of these sets can be approximated to arbitrary precision by diagonalizable elements within the same set.

Keywords: Quantum channel; Markovian channel; GKSL-generator; diagonalizable; Lie wedge