Single-photon quantum filtering with multiple measurements

TL;DR

This paper develops quantum filters for single-photon systems using multiple measurement types to enhance estimation accuracy, demonstrating improved excitation probabilities and revealing measurement back-action effects through simulations.

Contribution

It introduces filtering equations for a two-level quantum system with multiple measurement scenarios, advancing quantum filtering techniques for practical applications.

Findings

Multiple measurements improve atom excitation probability.

Simulation shows measurement back-action effects.

Different measurement configurations affect filtering performance.

Abstract

The single-photon quantum filtering problems have been investigated recently with applications in quantum computing. In practice, the detector responds with a quantum efficiency of less than unity since there exists some mode mismatch between the detector and the system, and the single-photon signal may be corrupted by quantum white noise. Consequently, quantum filters based on multiple measurements are designed in this paper to improve the estimation performance. More specifically, the filtering equations for a two-level quantum system driven by a single-photon input state and under multiple measurements are presented in this paper. Four scenarios, 1) two diffusive measurements with Q-P quadrature form, 2) two diffusive measurements with Q-Q quadrature form, 3) diffusive plus Poissonian measurements, and 4) two Poissonian measurements, are considered. It is natural to compare the filtering results, i.e., measuring single channel or both channels, which one is better? By the simulation where we use a single photon to excite an atom, it seems that multiple measurements enable us to excite the atom with higher probability than only measuring single channel. In addition, measurement back-action phenomenon is revealed by the simulation results.