Entanglement and Non-Markovianity of Quantum Evolutions

Abstract

We address the problem of quantifying the non-markovian character of quantum time evolutions of general systems in contact with an environment. We introduce two different measures of non-markovianity that exploit the specific traits of quantum correlations and are suitable for opposite experimental contexts. When complete tomographic knowledge about the evolution is available, our measure provides a necessary and sufficient condition to quantify strictly the non-markovianity. In the opposite case, when no information whatsoever is available, we propose a sufficient condition for non-markovianity. Remarkably, no optimization procedure underlies our derivation, which greatly enhances the practical relevance of the proposed criteria.

System–environment correlations and non-Markovian dynamics

“…The analysis has been based both on a single snapshot of the dynamics [17] and on the full time evolution of the open quantum system within a certain time interval [18,19]. In the latter approach, memory effects associated with non-Markovian dynamics are expected to cause temporary increase in the distinguishability of states (in terms of trace distance, e.g.…”

“…In the latter approach, memory effects associated with non-Markovian dynamics are expected to cause temporary increase in the distinguishability of states (in terms of trace distance, e.g. [18]) and the dynamics may no longer be divisible [19]. Under Markovian dynamics, on the other hand, the decay of distinguishability will be monotonic throughout and divisibility will be ensured.…”

Non-Markovian qubit dynamics in a circuit-QED setup

“…Memoryless or Markovian evolutions represent a limited portion of the rich scenario of open system dynamics. Much effort has then been directed to characterize, quantify and manipulate the degree of nonMarkovianity of physical systems [15]. In this work, we propose a circuit-QED simulation of spin-boson systems where inter-mode vibrational couplings can be induced and externally controlled.…”

Non-Markovian qubit dynamics induced by Coulomb crystals

“…A rigorous characterization for this class exists, based on the ability of describing the reduced system dynamics in terms of a semigroup of CPT dynamical maps [15]. A general definition of non-Markovian dynamics is more subtle and, as such, it has been the subject of intense recent studies [16][17][18]. Loosely speaking, non-Markovian behavior is characterized by memory effects, enabling the system to temporarily recover some of its genuine quantum properties.…”