Effective disentanglement of measured system and measurement apparatus

TL;DR

This paper derives exact expressions for the dynamics of a multi-level system coupled to a bosonic measurement device, revealing how entanglement transitions to classical correlation over time and identifying parameters influencing this process.

Contribution

It provides explicit formulas for expectation values in a coupled system and characterizes the effective disentanglement process, advancing understanding of measurement-induced correlations.

Findings

Systems become classically correlated over time despite entanglement.

Explicit separable state is derived for the coupled system.

Physical parameters controlling disentanglement timescales are identified.

Abstract

We consider a multi-level system coupled to a bosonic measurement apparatus. We derive exact expressions for the time-dependent expectation values of a large class of physically relevant observables that depend on degrees of freedom of both sytems. We find that, for this class, though the two systems become entangled as a result of their interaction, they appear classically correlated for long enough times. The unique corresponding separable state is determined explicitly. To better understand the physical parameters that control the time scale of this effective disentanglement process, we study a one-dimensional measurement apparatus.