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Journal of Physics B Atomic Molecular and Optical Physics

On the relationship between non-Markovianity and entanglement protection

Andrés Rosario Hamann, E. Massoni, F. De Zela

Published Apr 5, 2012• 12 citations

Abstract

We test the conjecture that non-Markovian dynamics may help to protect quantum entanglement. To this end, we address an open system whose environment behaves either as a quantal system or as an effective reservoir, depending on the regime chosen to rule the system–environment dynamics. This allows us to study entanglement dynamics within Markovian and non-Markovian regimes. We focus on the recently introduced definition of quantum non-Markovianity that is based on the trace distance between pairs of initial states. The corresponding quantum measure for assessing the non-Markovianity of a quantum map Φ is submitted to test. We report cases for which signals non-Markovianity, even though Φ belongs to a purely dissipative regime. We argue that is not generally applicable to assess the non-Markovianity of a quantum process, because information is not always encoded in a way that depends on the distinguishability between states. When entanglement is used as the carrier of information, non-Markovianity should be diagnosed in terms of an entanglement measure. We thus compare the dynamics of Wooters concurrence and of trace distance between states, showing that they may behave qualitatively alike but leading to conflicting diagnosis about the backflow of information from the environment to the system. In contrast to other studies, in our case entanglement is transferred only to potential carriers of information, thereby excluding paradoxical situations that involve entangled reservoirs.

DOI: 10.1088/0953-4075/45/9/095501

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The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behavior. Here, we review recent ideas developing a general mathematical definition for non-Markoviantiy in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system-environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system.

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