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

Author(s)

Malouf, William T. B. ^{[1, 2]} ; Goold, John ^[3] ; Adesso, Gerardo ^[2] ; Landi, Gabriel T. ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Fis, BR-05314970 Sao Paulo - Brazil

^[2] Univ Nottingham, Sch Math Sci, Univ Pk, Nottingham NG7 2RD - England

^[3] Trinity Coll Dublin, Sch Phys, Dublin 2 - Ireland

• Document type: Journal article
• Source: Journal of Physics A-Mathematical and Theoretical; v. 53, n. 30 JUL 31 2020.
• Web of Science Citations: 0

Abstract

The conditional mutual information (CMI) I(A : C vertical bar B) quantifies the amount of correlations shared between A and C 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. (AU)

• FAPESP's process: 17/06323-7 - Irreversibility and entropy production in Gaussian quantum systems
• Grantee: William Tiago Batista Malouf
• Support Opportunities: Scholarships in Brazil - Master
• FAPESP's process: 17/07973-5 - Thermodynamics and information technologies with continuous variable quantum systems
• Grantee: Gabriel Teixeira Landi
• Support Opportunities: Regular Research Grants
• FAPESP's process: 16/08721-7 - Stochastic modeling of non-equilibrium quantum systems
• Grantee: Gabriel Teixeira Landi
• Support Opportunities: Regular Research Grants
• FAPESP's process: 18/08211-4 - Quantum correlations and irreversibility
• Grantee: William Tiago Batista Malouf
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree