Average entropy and asymptotics

TL;DR

This paper analyzes the asymptotic behavior of the expected entanglement entropy in high tensor powers of holomorphic line bundles on complex manifolds, providing insights into quantum entanglement in geometric settings.

Contribution

It determines the asymptotic behavior of expected entanglement entropy as the tensor power N approaches infinity for holomorphic sections on complex manifolds.

Findings

Asymptotic formulas for expected entanglement entropy as N→∞

Connections between geometric line bundles and quantum entanglement

Quantitative descriptions of entropy growth in complex geometric settings

Abstract

We determine the $N\to \infty$ asymptotics of the expected value of entanglement entropy in $H_{1,N}\otimes H_{2,N}$, where $H_{1,N}$ and $H_{2,N}$ are the spaces of holomorphic sections of the $N$-th tensor powers of hermitian ample line bundles on compact complex manifolds.