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

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.