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Non-Markovianity through accessible information
F. F. Fanchini, G. Karpat, B. Çakmak, L. K. Castelano, G. H. Aguilar, O. Jiménez Farías, S. P. Walborn, P. H. Souto Ribeiro, M. C. de Oliveira
TL;DR
The paper addresses the missing entropic connection between non-Markovian behavior and information flow between a quantum system and its environment. It proposes an entanglement-based measure using accessible information and establishes its behavior through theory and an optical experiment. The results show that decreases in the environment’s accessible information signal non-Markovianity, with theoretical predictions confirmed experimentally.
Problem
The relationship between non-Markovian behavior and system–environment information flow through an entropic measure had not been established.
Method
The paper couples a system S to an apparatus A that interacts with an environment E, relating S–A entanglement of formation to the accessible information E acquires about S.
Results
A temporary decrease in the environment’s accessible information about S indicates non-Markovianity, and optical experiments confirm the theoretical predictions.
Takeaways & Limitations
The proposed measure connects entanglement growth between S and A with information flow from E to S through an entropic information measure.
Takeaways & Limitations
The analysis initially assumes a pure environment and uses the maximally entangled initial SA state as the optimal state.
Abstract
from arXiv · showhide
The degree of non-Markovianity of quantum processes has been characterized in several different ways in the recent literature. However, the relationship between the non-Markovian behavior and the flow of information between the system and the environment through an entropic measure has not been yet established. We propose an entanglement-based measure of non-Markovianity by employing the concept of assisted knowledge, where the environment E, acquires information about a system S, by means of its measurement apparatus A. The assisted knowledge, based on the accessible information in terms of von-Neumann entropy, monotonically increases in time for all Markovian quantum processes. We demonstrate that the signatures of non-Markovianity can be captured by the nonmonotonic behaviour of the assisted knowledge. We explore this scenario for a two-level system undergoing a relaxation process, through an experimental implementation using an optical approach that allows full access to the state of the environment.
SUPPLEMENTARY MATERIAL: Optimization of the Measure
The optimization reduces the relevant apparatus-state search to three real variables and shows that the measure depends only on the Bloch-vector length r. Across all bath parameters λ/γ0, the measure is maximized at r = 0, corresponding to a maximally mixed apparatus and maximally entangled system–apparatus state.
- Optimization: The optimization need not cover all six real parameters of a general pure two-qubit state; three real variables suffice without loss of generality.This simplification follows from entanglement invariance under local unitary operations and the absence of direct interaction between S and E.
- Optimization: The apparatus state is parameterized by a Bloch vector with length r satisfying |r| ≤ 1, while the measure is independent of its angular variables θ and φ.Thus, N(Λ) depends only on r rather than the full Bloch-vector direction.
- Measure dependence: Figure 3 plots N(Λ) against r and the bath parameter λ/γ0.
- Optimal state: For every λ/γ0, N(Λ) reaches its maximum at r = 0.
- Optimal state: At r = 0, the apparatus is maximally mixed and the bipartite system SA is maximally entangled.