Theory Framework of Multiplexed Photon-Number-Resolving Detectors

TL;DR

This paper develops a theoretical model for multiplexed photon-number-resolving detectors, demonstrating their advantages in quantum state generation and showing significant improvements in fidelity and success probability with feasible experimental parameters.

Contribution

The work introduces a new theoretical framework for multiplexed PNR detectors and proves their estimation error decreases inversely with the number of detectors, enabling practical quantum state engineering.

Findings

Estimation error decreases inversely with the number of detectors.

Achieves ~0.88 fidelity with 20 detectors at 95% efficiency.

Enables megahertz-rate cat-state generation with tens of detectors.

Abstract

Photon counting is a fundamental component in quantum optics and quantum information. However, implementing ideal photon-number-resolving (PNR) detectors remains experimentally challenging. Multiplexed PNR detection offers a scalable and practical alternative by distributing photons across multiple modes and detecting their presence using simple ON-OFF detectors, thereby enabling approximate photon-number resolution. In this work, we establish a theoretical model for such detectors and prove that the estimation error in terms of photon number moments decreases inverse proportionally to the number of detectors. Thanks to the enhanced PNR capability, multiplexed PNR detector provides an advantage in cat-state breeding protocols. Assuming a two-photon subtraction case, $7$dB of squeezing, and an array of 20 detectors of efficiency $95\%$, our calculation predicts fidelity $\sim0.88$ with a success probability $\sim 3.8\%$, representing orders-of-magnitude improvement over previous works. Similar enhancement also extends to cat-state generation with the generalized photon number subtraction. With experimentally feasible parameters, our results suggest that megahertz-rate cat-state generation is achievable using an on-chip array of \emph{tens} of ON-OFF detectors.