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Convex geometry of Markovian Lindblad dynamics and witnessing non-Markovianity by Bhattacharya, Bihalan; Bhattacharya, Samyadeb is a scholarly article available to read on EtoBox.

What is Convex geometry of Markovian Lindblad dynamics and witnessing non-Markovianity about?

We develop a theory of linear witnesses for detecting non-Markovianity, based on the geometric structure of the set of Choi states for all Markovian evolutions having Lindblad type generators. We show that the set of all such Markovian Choi states form a convex and compact set under the small time interval approximation. Invoking geometric Hahn-Banach theorem, we construct linear witnesses to separate a given non-Markovian Choi state from the set of Markovian Choi states. We present examples of such witnesses for dephasing channel and Pauli channel in case of qubits. We further investigate the geometric structure of the Markovian Choi states to find that they do not form a polytope. This presents a platform to consider non-linear improvement of non-Markovianity witnesses.

Author

Bhattacharya, Bihalan; Bhattacharya, Samyadeb

Published

2018

Language

EN