Spacetime mutual information

Quantum mutual information is the measure of correlations between two regions of a system, and is known to bound all the spatial correlations between two such regions. However, in experiments we also measure temporal correlations; where the latter are associated to dynamical properties such as thermalization, transport, and causal propagation of information. An immediate obstacle in generalizing quantum mutual information to time-like separated regions is that such regions are described by two different Hilbert spaces, which makes it less obvious to define what entanglement is. In this talk I will introduce a spacetime generalization of mutual information that overcomes this obstacle and generalizes several of the properties of standard mutual information; in particular it bounds spacetime correlation functions. Moreover, this quantity can be framed as a constrained version of the channel relative entropy used in quantum channel discrimination. I will also show that, in the context of many-body systems, the spacetime mutual information displays different asymptotic behaviors in time depending on whether the system thermalizes and has conserved quantities.