Analysis of the conditional mutual information in ballistic and diffusive non-equilibrium steady-states

Malouf, William Tiago Batista; Goold, John; Adesso, Gerardo; Landi, Gabriel

Abstract

The conditional mutual information (CMI) $\mathcal{I}(A\! : \! C|B)$ quantifies the amount of correlations shared between $A$ and $C$ \emph{given} $B$. It therefore functions as a more general quantifier of bipartite correlations in multipartite scenarios, playing an important role in the theory of quantum Markov chains. In this paper we carry out a detailed study on the behavior of the CMI in non-equilibrium steady-states (NESS) of a quantum chain placed between two baths at different temperatures. These results are used to shed light on the mechanisms behind ballistic and diffusive transport regimes and how they affect correlations between different parts of a chain. We carry our study for the specific case of a 1D bosonic chain subject to local Lindblad dissipators at the boundaries. In addition, the chain is also subject to self-consistent reservoirs at each site, which are used to tune the transport between ballistic and diffusive. As a result, we find that the CMI is independent of the chain size $L$ in the ballistic regime, but decays algebraically with $L$ in the diffusive case. Finally, we also show how this scaling can be used to discuss the notion of local thermalization in non-equilibrium steady-states.

Citation

Malouf, W. T. B., Goold, J., Adesso, G., & Landi, G. (2020). Analysis of the conditional mutual information in ballistic and diffusive non-equilibrium steady-states. Journal of Physics A: Mathematical and Theoretical, 53(30), Article 305302. https://doi.org/10.1088/1751-8121/ab93fd

• Journal Article Type: Article
• Acceptance Date: May 18, 2020
• Online Publication Date: May 18, 2020
• Publication Date: Jul 31, 2020
• Deposit Date: May 24, 2020
• Publicly Available Date: May 19, 2021
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 53
• Issue: 30
• Article Number: 305302
• DOI: https://doi.org/10.1088/1751-8121/ab93fd
• Keywords: Modelling and Simulation; Statistics and Probability; Mathematical Physics; General Physics and Astronomy; Statistical and Nonlinear Physics
• Public URL: https://nottingham-repository.worktribe.com/output/4500828
• Publisher URL: https://iopscience.iop.org/article/10.1088/1751-8121/ab93fd