Time-Continuous Bell Measurements

TL;DR

This paper introduces a framework for time-continuous Bell measurements, enabling real-time entanglement and quantum state transfer in complex systems, with broad applicability and robustness to losses.

Contribution

It derives stochastic Schrödinger and feedback master equations for continuous Bell measurements, expanding control techniques for quantum systems and networks.

Findings

Deterministic entanglement of two qubits via homodyne detection with 50% photon loss tolerance.

Continuous teleportation of quantum light states to mechanical oscillators.

Applicable to various physical systems and scalable to multiple systems and measurements.

Abstract

We combine the concept of Bell measurements, in which two systems are projected into a maximally entangled state, with the concept of continuous measurements, which concerns the evolution of a continuously monitored quantum system. For such time-continuous Bell measurements we derive the corresponding stochastic Schr\"odinger equations, as well as the unconditional feedback master equations. Our results apply to a wide range of physical systems, and are easily adapted to describe an arbitrary number of systems and measurements. Time-continuous Bell measurements therefore provide a versatile tool for the control of complex quantum systems and networks. As examples we show show that (i) two two-level systems can be deterministically entangled via homodyne detection, tolerating photon loss up to 50%, and (ii) a quantum state of light can be continuously teleported to a mechanical oscillator, which works under the same conditions as are required for optomechanical ground state cooling.