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arXiv:2601.13869 · Physical Review A

Nonclassical photocounting statistics with a single on-off detector

V. S. Kovtoniuk, M. Bohmann, A. A. Semenov

quant-phSubmitted Jan 20, 2026• Announced Jan 21, 2026• 0 citations
v1 · Jan 20, 2026v2 · Jun 18, 2026
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Abstract

Any single on-off photocounter, which can only detect the presence or absence of photons without discriminating their number, is not capable of identifying nonclassical nature of light. This limitation arises because any photocounting statistics obtained with such a detector can be easily reproduced with coherent states of a light mode. We show that a simple modification of an on-off detector -- introducing controlled attenuation as a tunable setting -- enables such detectors to reveal nonclassical properties of radiation fields.

Journal reference
Phys. Rev. A 113, 063726 (2026)
DOI
10.1103/pknl-24xd
Comments
15 pages, 8 figures

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Any single on-off photocounter, which can only detect the presence or absence of photons without discriminating their number, is not capable of identifying nonclassical nature of light. This limitation arises because any photocounting statistics obtained with such a detector can be easily reproduced with coherent states of a light mode. We show that a simple modification of an on-off detector -- introducing controlled attenuation as a tunable setting -- enables such detectors to reveal nonclassical properties of radiation fields.
We derive a closed photocounting formula, including noise counts and a finite quantum efficiency, for photon-number-resolving detectors based on on-off detectors. It applies to detection schemes such as array detectors and multiplexing setups. The result renders it possible to compare the corresponding measured counting statistics with the true photon number statistics of arbitrary quantum states. The photocounting formula is applied to the discrimination of photon numbers of Fock states, squeezed states, and odd coherent states. It is illustrated for coherent states that our formula is indispensable for the correct interpretation of quantum effects observed with such devices.
Reconstruction of photon statistics of optical states provides fundamental information on the nature of any optical field and finds various relevant applications. Nevertheless, no detector that can accurately discriminate the number of incident photons is available, whereas reconstruction by quantum tomography is not an easily implementable technique suited for a diffuse use. Even if on/off detectors, as usual avalanche photodiodes operating in Geiger mode, seem useless as photocounters, recently it was shown that reconstruction of photon statistics is possible by considering variable quantum efficiency. We have experimentally demonstrated the potential of this technique by reconstructing photon statistics for various optical fields both in the cw and pulsed regime ranging from heralded photon states to multi-thermal and coherent ones. In this paper, after having introduced the method, a review of the results obtained for the mono-partite case is given and the extension to bi-partite case is presented in detail.
In quantum optics, measurement statistics---for example, photocounting statistics---are considered nonclassical if they cannot be reproduced with statistical mixtures of classical radiation fields. We have formulated a necessary and sufficient condition for such nonclassicality. This condition is given by a set of inequalities that tightly bound the convex set of probabilities associated with classical electromagnetic radiation. Analytical forms for full sets and subsets of these inequalities are obtained for important cases of realistic photocounting measurements and unbalanced homodyne detection. As an example, we consider photocounting statistics of phase-squeezed coherent states. Contrary to a common intuition, the analysis developed here reveals distinct nonclassical properties of these statistics that can be experimentally corroborated with minimal resources.
We study the properties of a photodetector that has a numberresolving capability. In the absence of dark counts, due to its finite quantum efficiency, photodetection with such a detector can only eliminate the possibility that the incident field corresponds to a number of photons less than the detected photon number. We show that such a non-photon number-discriminating detector, however, provides a useful tool in the reconstruction of the photon number distribution of the incident field even in the presence of dark counts.
We present a general method to detect nonclassical radiation fields with systems of on-off detectors. We especially study higher order correlations for the identification of nonclassical radiation. This allows us to directly characterize quantum correlations by the statistics measured with systems of on-off detectors. Additionally, we generalize our method to multiple detector systems for measurements of correlations between light fields. We also consider multimode radiation fields and isolate nonclassicality in terms of the space time correlations. Finally, we present results for the quantum statistics using on-off detectors operating in nonlinear detection modes.