Linear-optical processing cannot increase photon efficiency

TL;DR

Linear-optical processing cannot enhance photon efficiency or single-photon fidelity beyond certain fundamental limits, even with complex interferometry and conditioning, when no multiphoton components are introduced.

Contribution

The paper proves that linear-optical processing cannot improve photon efficiency or fidelity beyond the efficiency of the best source, establishing fundamental limits.

Findings

Single-photon fraction cannot exceed source efficiency without multiphoton components.

With multiphoton components, fidelity cannot surpass 1/2.

Quantum-optical state efficiency cannot be increased by linear optics.

Abstract

We answer the question whether linear-optical processing of the states produced by one or multiple imperfect single-photon sources can improve the single-photon fidelity. This processing can include arbitrary interferometers, coherent states, feedforward, and conditioning on results of detections. We show that without introducing multiphoton components, the single-photon fraction in any of the single-mode states resulting from such processing cannot be made to exceed the efficiency of the best available photon source. If multiphoton components are allowed, the single-photon fidelity cannot be increased beyond 1/2. We propose a natural general definition of the quantum-optical state efficiency, and show that it cannot increase under linear-optical processing.