Entanglement of a pair of quantum emitters via continuous fluorescence measurements: a tutorial

TL;DR

This tutorial reviews recent measurement-based protocols for generating entanglement between remote quantum emitters through continuous fluorescence detection, analyzing different measurement schemes and their effectiveness.

Contribution

It provides a unified theoretical framework for understanding entanglement generation via continuous measurements, extending previous analyses and including bounds on entanglement speed and efficiency.

Findings

Homodyne detection can produce entanglement comparable to photodetection.

Derived bounds on the fastest Bell state preparation under joint measurement.

Characterized maximal entanglement yield with lossy measurement conditions.

Abstract

We discuss recent developments in measurement protocols that generate quantum entanglement between two remote qubits, focusing on the theory of joint continuous detection of their spontaneous emission. We consider a device geometry similar to that used in well-known Bell-state measurements, which we analyze using a conceptually transparent model of stochastic quantum trajectories; we use this to review photodetection, the most straightforward case, and then generalize to the diffusive trajectories from homodyne and heterodyne detection as well. Such quadrature measurement schemes are a realistic two-qubit extension of existing circuit-QED experiments which obtain quantum trajectories by homodyning or heterodyning a superconducting qubit's spontaneous emission, or an adaptation of existing optical measurement schemes to obtain jump trajectories from emitters. We mention key results, presented from within a single theoretical framework, and draw connections to concepts in the wider literature on entanglement generation by measurement (such as path information erasure and entanglement swapping). The photon which-path information acquisition, and therefore the two-qubit entanglement yield, is tunable under the homodyne detection scheme we discuss, at best generating equivalent average entanglement dynamics as in the comparable photodetection case. In addition to deriving this known equivalence, we extend past analyses in our characterization of the measurement dynamics: We include derivations of bounds on the fastest possible evolution towards a Bell state under joint homodyne measurement dynamics, and characterize the maximal entanglement yield possible using inefficient (lossy) measurements.