On the theoretical prospects of multiport devices for photon-number-resolving detections

TL;DR

This paper provides a theoretical analysis of multiport devices for photon-number-resolving detection, establishing their potential to approach ideal Fock-state measurements and examining the impact of photon losses on their performance.

Contribution

It introduces a general analytical framework for assessing the tomographic accuracy of multiport devices and characterizes their performance with finite and infinite output ports, including effects of photon losses.

Findings

Infinite multiport devices can emulate Fock-state measurements without photon losses.

Photon losses cause multiport devices to perform as binomial mixtures of Fock-state measurements.

Analytical formulas for transfer functions are provided for finite and infinite output ports.

Abstract

Ideal photon-number-resolving detectors form a class of important optical components in quantum optics and quantum information theory. In this article, we theoretically investigate the potential of multiport devices having reconstruction performances approaching that of the Fock-state measurement. By recognizing that all multiport devices are minimally complete, we first provide a general analytical framework to describe the tomographic accuracy (or quality) of these devices. Next, we show that a perfect multiport device with an infinite number of output ports functions as either the Fock-state measurement when photon losses are absent or binomial mixtures of Fock-state measurements when photon losses are present, and derive their respective expressions for the tomographic transfer function. This function is the scaled asymptotic mean squared-error of the reconstructed photon-number distributions uniformly averaged over all distributions in the probability simplex. We then supply more general analytical formulas for the transfer function for finite numbers of output ports in both the absence and presence of photon losses. The effects of photon losses on the photon-number resolving power of both infinite- and finite-size multiport devices are also investigated.