Coherent state superpositions, entanglement and gauge/gravity correspondence

TL;DR

This paper explores coherent states in gauge/gravity correspondence, analyzing their entanglement, quantum Fisher information, and the effects of noise, revealing their relation to Young tableau states and phase space geometry.

Contribution

It introduces a detailed analysis of coherent states, entanglement, and noise effects within gauge/gravity duality, connecting quantum states to geometric features in phase space.

Findings

N-state Schrödinger cat states approach Young tableau states at large N.

Quantum Fisher information relates to energy variance and state localizability.

Entanglement correlates with phase space geometry, such as annulus area between rings.

Abstract

We focus on two types of coherent states, the coherent states of multi graviton states and the coherent states of giant graviton states, in the context of gauge/gravity correspondence. We conveniently use a phase shift operator and its actions on the superpositions of these coherent states. We find $N$-state Schrodinger cat states which approach the one-row Young tableau states, with fidelity between them asymptotically reaches 1 at large $N$. The quantum Fisher information of these states is proportional to the variance of the excitation energy of the underlying states, and characterizes the localizability of the states in the angular direction in the phase space. We analyze the correlation and entanglement between gravitational degrees of freedom using different regions of the phase space plane in bubbling AdS. The correlation between two entangled rings in the phase space plane is related to the area of the annulus between the two rings. We also analyze two types of noisy coherent states, which can be viewed as interpolated states that interpolate between a pure coherent state in the noiseless limit and a maximally mixed state in the large noise limit.