Holographic Weak Measurement

TL;DR

This paper explores a holographic model of weak measurements in conformal field theories, revealing how such measurements influence entanglement and geometry, including phase transitions and complex spacetime structures.

Contribution

It introduces a holographic framework for weak measurements in CFTs using interface branes, connecting weak measurements to interface CFTs and analyzing their geometric and entanglement properties.

Findings

Holographic entanglement entropy matches between ICFT and weak measurement models.

Weak measurements induce a rich phase diagram with distinct geometric configurations.

Post-measurement geometries can exhibit complex structures like Python's lunch.

Abstract

In this paper, we study a holographic description of weak measurements in conformal field theories (CFTs). Weak measurements can be viewed as a soft projection that interpolates between an identity operator and a projection operator, and can induce an effective central charge distinct from the unmeasured CFT. We model the weak measurement by an interface brane, separating different geometries dual to the post-measurement state and the unmeasured CFT, respectively. In an infinite system, the weak measurement is related to ICFT via a spacetime rotation. We find that the holographic entanglement entropy with twist operators located on the defect is consistent in both calculations for ICFT and weak measurements. We additionally calculate the boundary entropy via holographic entanglement as well as partition function. In a finite system, the weak measurement can lead to a rich phase diagram: for marginal measurements the emergent brane separates two AdS geometries, while for irrelevant measurements the post-measurement geometry features an AdS spacetime and a black hole spacetime that are separated by the brane. Although the measurement is irrelevant in the later phase, the post-measurement geometry can realize a Python's lunch.