# Quantum vs. classical information: operator negativity as a probe of scrambling

## TL;DR

This paper investigates the behavior of operator negativity as a measure of quantum scrambling across various theoretical models, revealing signatures of maximal scrambling and differences between quantum and classical information dynamics.

## Contribution

It introduces an effective line-tension model for logarithmic negativity in ergodic systems and explores the connection between partial transpose operations and holographic entanglement measures.

## Key findings

- Holographic systems show maximal scrambling signatures.
- Random circuits mimic holographic channel behavior.
- Negativity dynamics differ from mutual information, indicating distinct quantum and classical information behaviors.

## Abstract

We consider the logarithmic negativity and related quantities of time evolution operators. We study free fermion, compact boson, and holographic conformal field theories (CFTs) as well as numerical simulations of random unitary circuits and integrable and chaotic spin chains. The holographic behavior strongly deviates from known non-holographic CFT results and displays clear signatures of maximal scrambling. Intriguingly, the random unitary circuits display nearly identical behavior to the holographic channels. Generically, we find the "line-tension picture" to effectively capture the entanglement dynamics for ergodic systems and the "quasi-particle picture" for integrable systems. With this motivation, we propose an effective line-tension that captures the dynamics of the logarithmic negativity in ergodic systems in the spacetime scaling limit. We compare the negativity and mutual information leading us to find distinct dynamics of quantum and classical information. The "spurious entanglement" we observe may have implications on the "simulatability" of quantum systems on classical computers. Finally, we elucidate the connection between the operation of partially transposing a density matrix in conformal field theory and the entanglement wedge cross section in Anti-de Sitter space using geodesic Witten diagrams.