Convex geometry of Markovian Lindblad dynamics and witnessing non-Markovianity

Understand

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.