Observable and computable entanglement in time

TL;DR

This paper introduces a new family of entanglement measures for time-separated quantum subsystems, applicable across various quantum systems, and demonstrates their utility through theoretical bounds and experimental validation.

Contribution

It proposes novel entanglement measures for time-separated regions, applicable to continuous and discrete systems, and connects them to timelike pseudoentropy with experimental validation.

Findings

Derived bounds on time-separated correlation functions

Validated measurement protocols on IBM quantum device

Performed explicit computations in multiple quantum models

Abstract

We propose a novel family of entanglement measures for time-separated subsystems. Our definitions are applicable to any quantum system, continuous or discrete. To illustrate their utility, we derive upper and lower bounds on time-separated correlation functions, akin to the bound on spatially separated correlators in terms of the mutual information. In certain cases our bounds are tight. For relativistic quantum field theories our definition agrees with the analytic continuation from spacelike to timelike separated regions. We provide relevant measurement protocols and execute them on the IBM quantum device ibm_sherbrooke for a simple qubit system. Also we perform explicit computations for an Ising spin chain, free fermions, (1+1)-dimensional conformal field theories and holographic theories. Finally we explain how the proposed entanglement in time provides a microscopic definition for the recently introduced timelike pseudoentropy.