Locally accessible information of holographic states*

In quantum gravity, a crucial question is how much information about a subsystem can be learned from another. This is particularly relevant in studies like black hole information recovery. In this work, we focus on locally accessible information, which quantifies the information gain about a subsystem through the optimal measurement on the other. Our work explores the gravity dual of this quantity. Interestingly, a phase that appears to the leading order analysis in the semiclassical calculation is in tension with what we usually expect from finite-dimensional quantum systems. However, the random state calculation suggests that these conflicts might be resolved by considering nonperturbative effects. Since a finite-dimensional system, semiclassical subsystem, and a subsystem in quantum gravity are each tied to different types of von Neumann algebras, our study on locally accessible information might be useful to understand and differentiate these types from a specific, information theoretic quantity.