# Detecting topology change via correlations and entanglement from gauge/gravity correspondence

## TL;DR

This paper investigates how entanglement measures and correlations in Young tableau states can reveal the topology of dual spacetime geometries within gauge/gravity correspondence, introducing new bounds and state overlaps.

## Contribution

It provides a novel method to detect topology changes via entanglement and correlation functions in gauge/gravity duality, including bounds on state overlaps and superpositions.

## Key findings

- Topologically distinct geometries can be generated by superposing trivial topology states.
- A refined exponential bound on overlaps between coherent and Young tableau states is established.
- Overlap norms are bounded by inverse powers of entanglement entropy exponential.

## Abstract

We compute a momentum space version of the entanglement spectrum and entanglement entropy of general Young tableau states, and one-point functions on Young tableau states. These physical quantities are used to measure the topology of the dual spacetime geometries in the context of gauge/gravity correspondence. The idea that Young tableau states can be obtained by superposing coherent states is explicitly verified. In this quantum superposition, a topologically distinct geometry is produced by superposing states dual to geometries with a trivial topology. Furthermore we have a refined bound for the overlap between coherent states and the rectangular Young tableau state, by using the techniques of symmetric groups and representations. This bound is exponentially suppressed by the total edge length of the Young tableau. It is also found that the norm squared of the overlaps is bounded above by inverse powers of the exponential of the entanglement entropies. We also compute the overlaps between Young tableau states and other states including squeezed states and multi-mode entangled states which have similarities with those appeared in quantum information theory.