Monitoring-induced Entanglement Entropy and Sampling Complexity

TL;DR

This paper explores how monitoring schemes in open quantum systems influence entanglement and sampling complexity, linking measurement-induced entanglement to the computational hardness of quantum sampling tasks.

Contribution

It demonstrates how specific monitoring schemes induce entanglement in quantum trajectories and connects this to the complexity of boson sampling.

Findings

Monitoring affects entanglement in quantum trajectories

Click registration induces entanglement in emitter arrays

Sampling complexity relates to trajectory entanglement scaling

Abstract

The dynamics of open quantum systems is generally described by a master equation, which describes the loss of information into the environment. By using a simple model of uncoupled emitters, we illustrate how the recovery of this information depends on the monitoring scheme applied to register the decay clicks. The dissipative dynamics, in this case, is described by pure-state stochastic trajectories and we examine different unravelings of the same master equation. More precisely, we demonstrate how registering the sequence of clicks from spontaneously emitted photons through a linear optical interferometer induces entanglement in the trajectory states. Since this model consists of an array of single-photon emitters, we show a direct equivalence with Fock-state boson sampling and link the hardness of sampling the outcomes of the quantum jumps with the scaling of trajectory entanglement.