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

TL;DR

This paper investigates how the conditional mutual information behaves in quantum chains under non-equilibrium conditions, revealing distinct scaling laws in ballistic versus diffusive transport regimes and implications for local thermalization.

Contribution

It provides a detailed analysis of CMI in quantum chains, demonstrating size-independent behavior in ballistic regimes and algebraic decay in diffusive regimes, linking correlations to transport properties.

Findings

CMI is size-independent in ballistic transport

CMI decays algebraically in diffusive transport

Scaling of CMI informs about local thermalization

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.