Notes on Pseudo Entropy Amplification

TL;DR

This paper investigates pseudo entropy in various quantum systems, revealing conditions under which it can be significantly amplified, and discusses implications for holographic CFTs and the analogy with weak value amplification.

Contribution

It introduces the concept of pseudo entropy amplification, analyzing its occurrence in qubit systems and conformal field theories, and compares it to weak value amplification.

Findings

Pseudo entropy can be parametrically large compared to the log of Hilbert space dimension.

Pseudo entropy amplification is analogous to weak value amplification.

Holographic CFTs do not exhibit amplification when non-perturbative effects are negligible.

Abstract

We study pseudo entropy for a particular linear combination of entangled states in qubit systems, two-dimensional free conformal field theories (CFT), and two-dimensional holographic CFT. We observe phenomena that the pseudo entropy can be parametrically large compared with the logarithm of the dimension of Hilbert space. We call these phenomena pseudo entropy amplification. The pseudo entropy amplification is analogous to the amplification of the weak value. In particular, our result suggests the holographic CFT does not lead the amplification as long as the non-perturbative effects are negligible. We also give a heuristic argument when such (non-)amplification can occur.