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.
Highlights
Photon-number-resolving (PNR) detection schemes are measurements that play a vital role in quantum information theory
The result in Equation (33) assigns a number to the average performance of a multiport device of arbitrary number of output ports s, port efficiencies {ηj} and loss probability based on statistical estimation theory
We present a short series of studies related to the performance of multiport devices on photon-number distribution tomography
Summary
Photon-number-resolving (PNR) detection schemes are measurements that play a vital role in quantum information theory.
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