Gravity dualities of quantum distances

TL;DR

This paper establishes gravity dualities for key quantum distances using cosmic branes and Euclidean on-shell actions, verified through 2D conformal field theory examples, linking quantum information measures with gravitational descriptions.

Contribution

It demonstrates gravity dualities for multiple quantum distances and a quasi-distance, providing two equivalent gravitational descriptions and validating them with conformal field theory calculations.

Findings

Gravity dualities for trace, Fubini-Study, Bures distances, and Rènyi relative entropy.

Dualities described by cosmic brane area and Euclidean on-shell action.

Exact match with conformal field theory computations.

Abstract

By choosing modular ground state as the reference state, this paper finds that three most frequently-used distances and a quantum quasi-distance, i.e. the trace distance, Fubini-Study distance, Bures distance and R\'{e}nyi relative entropy, all have gravity dualities. Their gravity dualities have two equivalent descriptions: one is given by the integration of the area of a cosmic brane, the other one is given by the Euclidian on-shell action of dual theory and the area of the cosmic brane. It then applies these dualities into the 2-dimensional conformal field theory as examples and finds the results match with the computations of field theory exactly.