Entanglement Dynamics of the Non-Unitary Holographic Channel

TL;DR

This paper investigates the entanglement dynamics in a non-unitary holographic quantum circuit with measurements, revealing new fractional growth behavior and the impact on non-local correlations, supported by a proposed gravity dual model.

Contribution

It introduces a novel dynamical behavior of operator entanglement with fractional coefficients and proposes a gravity dual and line-tension model for strongly scrambling circuits with measurements.

Findings

Operator entanglement exhibits fractional linear growth.

Projective measurements can destroy non-local correlations.

A gravity dual and line-tension model describe the circuit dynamics.

Abstract

We study the dynamical properties of a strongly scrambling quantum circuit involving a projective measurement on a finite-sized region by studying the operator entanglement entropy and mutual information (OEE and BOMI) of the dual operator state that corresponds to this quantum circuit. The time-dependence of the OEE exhibits a new dynamical behavior of operator entanglement, namely an additional fractional coefficient that accompanies the linear time growth of the OEE. For a holographic system, this is equivalent to an additional fractional coefficient that modifies the linear growth rate of the wormhole volume. The time-dependence of the BOMI shows that the projective measurement may destroy the non-local correlations in this dual state. We also propose a gravity dual as well as a line-tension picture, which is an effective model, that describe this strongly scrambling quantum circuit.