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arXiv:1004.2184 · Europhysics Letters (EPL)

Witness for initial system-environment correlations in open-system dynamics

E.-M. Laine, Jyrki Piilo, Heinz‐Peter Breuer

Published Dec 1, 2010• 156 citations
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Abstract

We study the evolution of a general open quantum system when the system and its environment are initially correlated. We show that the trace distance between two states of the open system can increase above its initial value, and derive tight upper bounds for the growth of the distinguishability of open-system states. This represents a generalization of the contraction property of quantum dynamical maps. The obtained inequalities can be interpreted in terms of the exchange of information between the system and the environment, and lead to a witness for system-environment correlations which can be determined through measurements on the open system alone.

DOI
10.1209/0295-5075/92/60010

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We study the evolution of a general open quantum system when the system and its environment are initially correlated. We show that the trace distance between two states of the open system can increase above its initial value, and derive tight upper bounds for the growth of the distinguishability of open-system states. This represents a generalization of the contraction property of quantum dynamical maps. The obtained inequalities can be interpreted in terms of the exchange of information between the system and the environment, and lead to a witness for system-environment correlations which can be determined through measurements on the open system alone.
A quantum system inevitably interacts with its surroundings. In general, one does not have detailed information on an environment. Identifying the environmental features can help us to control the environment and its effects on the dynamics of an open system. Here, we consider a tripartite system and introduce a witness for the initial correlations among environments by means of the concept of the trace distance. Due to the existence of the initial environmental correlations, a tight upper bound is obtained for the growth of the trace distance of open quantum system states. Therefore, the initial correlations among the environments subject to particular conditions can be detected by measurements on the open system.
We study the time evolution of four distance measures in the presence of initial system-environment correlations. It is well known that the trace distance between two quantum states of an open system may increase due to initial correlations, which leads to a breakdown of the contractivity of the reduced dynamics. Here we compare and analyze, for two different models, the time evolution of the trace distance, the Bures metric, the Hellinger distance, and the Jensen-Shannon divergence regarding an increase above their initial values, witnessing initial correlations. This work generalizes, deepens, and corrects a part of the study performed by Dajka et al. [Phys. Rev. A 84, 032120 (2011)] and thereby reveals generic features of the considered distance measures with respect to the capability of detecting initial system-environment correlations.
We show the connection between a witness that detects dynamical maps with initial system-environment correlations and a witness that detects non-Markovian open quantum systems. Our analysis is based on studying the role that state preparation plays in witnessing violations of contractivity of open-quantum-system dynamics. Contractivity is a property of some quantum processes where the trace distance of density matrices decrease with time. From this, we show how a witness of initial correlations is an upper bound to a witness of non-Markovianity. We discuss how this relationship shows further connections between initial system-environment correlations and non-Markovianity, at an instance of time, in open quantum systems.
The trace distance between two states of an open quantum system quantifies their distinguishability and, for a fixed environmental state, can increase above its initial value only in the presence of initial system-environment correlations. We provide experimental evidence of such a behavior. In our all-optical apparatus, we exploit spontaneous parametric down conversion as a source of polarization entangled states and a spatial light modulator to introduce in a general fashion correlations between the polarization and the momentum degrees of freedom, which act as environment.
The exchange of information between an open quantum system and its environment allows us to discriminate among different kinds of dynamics, in particular detecting memory effects to characterize non-Markovianity. Here, we investigate the role played by the system-environment correlations and the environmental evolution in the flow of information. First, we derive general conditions ensuring that two generalized dephasing microscopic models of the global system-environment evolution result exactly in the same open-system dynamics, for any initial state of the system. Then, we use the trace distance to quantify the distinct contributions to the information inside and outside the open system in the two models. Our analysis clarifies how the interplay between system-environment correlations and environmental-state distinguishability can lead to the same information flow from and toward the open system, despite significant qualitative and quantitative differences at the level of the global evolution.
The time evolution of the trace distance between two states of an open quantum system may increase due to initial system-environment correlations, thus exhibiting a breakdown of distance contractivity of the reduced dynamics. We analyze how the time evolution of the distance depends on the chosen distance measure. Here we elucidate the behavior of the trace distance, the Hilbert-Schmidt distance, the Bures distance, the Hellinger distance, and the quantum Jensen-Shannon divergence for two system-environment setups, namely a qubit bilinearly coupled to an infinite and a finite-size environment with the latter composed of harmonic oscillators.