Quantifying entanglement in multipartite conditional states of open quantum systems by measurements of their photonic environment

TL;DR

This paper uncovers a fundamental relation linking measurement outcomes and entanglement in open quantum systems, enabling direct experimental quantification of entanglement through environment measurements.

Contribution

It introduces a scaling law connecting measurement probabilities and entanglement in conditional states, facilitating entanglement detection via bath quantum tomography.

Findings

Derived a scaling law between entanglement and measurement outcomes.

Constructed entanglement distribution over measurement ensembles.

Provided rigorous results on finite-time disentanglement in non-Markovian systems.

Abstract

A key lesson of the decoherence program is that information flowing out from an open system is stored in the quantum state of the surroundings. Simultaneously, quantum measurement theory shows that the evolution of any open system when its environment is measured is nonlinear and leads to pure states conditioned on the measurement record. Here we report the discovery of a fundamental relation between measurement and entanglement which is characteristic of this scenario. It takes the form of a scaling law between the amount of entanglement in the conditional state of the system and the probabilities of the experimental outcomes obtained from measuring the state of the environment. Using the scaling, we construct the distribution of entanglement over the ensemble of experimental outcomes for standard models with one open channel and provide rigorous results on finite-time disentanglement in systems coupled to non-Markovian baths. The scaling allows the direct experimental detection and quantification of entanglement in conditional states of a large class of open systems by quantum tomography of the bath.