Inequivalence of Correlation-based Measures of Non-Markovianity

Abstract

We conclusively show that the entanglement- and the mutual information-based measures of quantum non-Markovianity are inequivalent. To this aim, we first analytically solve the optimization problem in the definition of the entanglement-based measure for a two-level system. We demonstrate that the optimal initial bipartite state of the open system and the ancillary is always given by one of the Bell states for any one qubit dynamics. On top of this result, we present an explicit example dynamics where memory effects emerge according to the mutual information-based measure, even though the time evolution remains memoryless with respect to the entanglement-based measure. Finally, we explain this disagreement between the two measures in terms of the information dynamics of the open system, exploring the accessible and inaccessible parts of information.

5 pages, 3 figures

References in corpus (4)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Non-Markovian effects on the dynamics of entanglement
• A Factorization Law for Entanglement Decay
• Non-Markovianity through flow of information between a system and an environment

Cited by in corpus (13)

• Non-Markovianity, coherence and system-environment correlations in a long-range collision model
• Enabling quantum non-Markovian dynamics by injection of classical colored noise
• Synchronization and Non-Markovianity in open quantum systems
• Estimating the degree of non-Markovianity using machine learning
• Entanglement negativity as a universal non-Markovianity witness
• Entropic and trace distance based measures of non-Markovianity
• Non-Markovianity Quantifier of an Arbitrary Quantum Process
• Kernel-based quantum regressor models learn non-Markovianity
• Memory in quantum processes with indefinite time direction and causal order
• Non-markovianity and bound states in quantum walks with a phase impurity
• Non-Markovian dynamics of the electronic subsystem in a laser-driven molecule: Characterization and connections with electronic-vibrational entanglement and electronic coherence
• Analytical results for the quantum non-Markovianity of spin ensembles undergoing pure dephasing dynamics
• Estimating the degree of non-Markovianity using variational quantum circuits