Estimating the decoherence time using non-commutative Functional Inequalities

Understand

We generalize the notions of the non-commutative Poincar\'e and modified log-Sobolev inequalities for primitive quantum Markov semigroups (QMS) to not necessarily primitive ones.

• These two inequalities provide estimates on the decoherence time of the evolution.
• More precisely, we focus on an algebraic definition of environment-induced decoherence in open quantum systems which happens to be generic on finite dimensional systems and describes the asymptotic behavior of any QMS.
• An essential tool in our analysis is the explicit structure of the decoherence-free algebra generated by the QMS, a central object in the study of passive quantum error correction schemes.