Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1601.05831

Theory of multiplexed photon number discrimination

Filippo M. Miatto, Akbar Safari, Robert W. Boyd

Published Jan 21, 2016• 3 citations
arXivHTMLPDF

Abstract

Although some non-trivial photon number resolving detectors exist, it may still be convenient to discriminate photon number states with the method of multiplexed detection. Multiplexing can be performed with paths in real space, with paths in time, and in principle with any degree of freedom that has a sufficient number of eigenstates and that can be coupled to the photon number. Previous works have addressed the probabilities involved in these measurements with Monte Carlo simulations, or by restricting the number of detectors to powers of 2, or without including quantum efficiency or noise. In this work we find an analytical expression of the detection probabilities for any number of input photons and any number of on/off photon detectors with a quantum efficiency $0\%\leqη\leq100\%$ and a false count probability $\varepsilon\geq0$. This allows us to retrodict the number of photons that we had at the input in the least unbiased way possible. We conclude our work with some examples.

DOI
10.48550/arxiv.1601.05831

Related papers

Explicit formulas for photon number discrimination with on/off detectors

Filippo M. Miatto, Akbar Safari, Robert W. Boyd

Discriminating between Fock states with a high degree of accuracy is a desirable feature for modern applications of optical quantum information processing. A well-known alternative to sophisticated photon number discriminating detectors is to split the field among a number of simple on/off detectors and infer the desired quantity from the measurement results. In this work we find an explicit analytical expression of the detection probability for any number of input photons, any number of on/off detectors, and we include quantum efficiency and a false count probability. This allows us to explicitly invert the conditional probability using Bayes' theorem and express the number of photons that we had at the input in the most unbiased way possible with ready-to-use formulas. We conclude with some examples.

Applied Optics•Aug 3, 2018•5 citations

Absolute calibration of single-photon and multiplexed photon-number-resolving detectors

Lior Cohen, Y. Pilnyak, D. Istrati +3 more

Single-photon detectors are widely used in modern quantum optics experiments and applications. Like all detectors, it is important for these devices to be accurately calibrated. A single-photon detector is calibrated by determining its detection efficiency; the common method to measure this quantity requires comparison to another detector. Here, we suggest a method to measure the detection efficiency of a single-photon detector without requiring an external reference detector. Our method is valid for individual single-photon detectors as well as multiplexed detectors, which are known to be photon number resolving. The method exploits the even-number photon-statistics of a nonlinear source, as well as the nonlinear loss of a single-photon detector that occurs when multiple photons are incident simultaneously. We have analytically modeled multiplexed detectors and used the results to experimentally demonstrate the calibration of a single-photon detector without the need for an external reference detector.

arXiv:1711.03594•Physical Review A•Jul 5, 2018•27 citations

True photocounting statistics of multiple on-off detectors

Jan Sperling, W. Vogel, G. S. Agarwal

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.

arXiv:1202.5106•Physical Review A•Feb 17, 2012•147 citations

Non-deterministic approximation of photon number discriminating detectors using non-discriminating detectors

Peter P. Rohde

We present a scheme for non-deterministically approximating photon number resolving detectors using non-discriminating detectors. The model is simple in construction and employs very few physical resources. Despite its non-determinism, the proposal may nonetheless be suitable for use in some quantum optics experiments in which non-determinism can be tolerated. We analyse the detection scheme in the context of an optical implementation of the controlled-NOT gate, an inherently non-deterministic device. This allows the gate's success probability to be traded away for improved gate fidelity, assuming high efficiency detectors. The scheme is compared to two other proposals, both deterministic, for approximating discriminating detectors using non-discriminating detectors: the cascade and time division multiplexing schemes.

arXiv:quant-ph/0411114•Journal of Optics B Quantum and Semiclassical Optics•Jan 29, 2005•7 citations

Benchmarking photon number resolving detectors

Jan Provazník, Lukáš Lachman, Radim Filip +1 more

Photon number resolving detectors are the ultimate measurement of quantum optics, which is the reason why developing the technology is getting significant attention in recent years. With this arises the question of how to evaluate the performance of the detectors. We suggest that performance of a photon number detector can be evaluated by comparing it to a multiplex of on-off detectors in a practical scenario: conditional preparation of a photon number state. Here, both the quality of the prepared state and the probability of the preparation are limited by the number of on-off detectors in the multiplex, which allows us to set benchmarks that can be achieved or surpassed by the photon number resolving detectors.

arXiv:2005.02093•Optics Express•Apr 13, 2020•49 citations

Evaluating the performance of photon-number-resolving detectors

Mattias Jönsson, Gunnar G. Bjork

We analyze the performance of photon-number-resolving (PNR) detectors and introduce a figure of merit for the accuracy of such detectors. This figure of merit is the (worst-case) probability that the photon-number-resolving detector correctly predicts the input photon number. Simulations of various PNR detectors based on multiplexed single-photon ``click detectors'' is performed. We conclude that the required quantum efficiency is very high in order to achieve even moderate (up to a handful) photon resolution, we derive the required quantum efficiency as a function of the the maximal photon number one wants to resolve, and we show that the number of click detectors required grows quadratically with the maximal number of photons resolvable.

arXiv:1812.05422•Physical Review A•Apr 16, 2019•53 citations
Although some non-trivial photon number resolving detectors exist, it may still be convenient to discriminate photon number states with the method of multiplexed detection. Multiplexing can be performed with paths in real space, with paths in time, and in principle with any degree of freedom that has a sufficient number of eigenstates and that can be coupled to the photon number. Previous works have addressed the probabilities involved in these measurements with Monte Carlo simulations, or by restricting the number of detectors to powers of 2, or without including quantum efficiency or noise. In this work we find an analytical expression of the detection probabilities for any number of input photons and any number of on/off photon detectors with a quantum efficiency 0%≤η≤100%0\%\leqη\leq100\%0%≤η≤100% and a false count probability ε≥0\varepsilon\geq0ε≥0. This allows us to retrodict the number of photons that we had at the input in the least unbiased way possible. We conclude our work with some examples.
Discriminating between Fock states with a high degree of accuracy is a desirable feature for modern applications of optical quantum information processing. A well-known alternative to sophisticated photon number discriminating detectors is to split the field among a number of simple on/off detectors and infer the desired quantity from the measurement results. In this work we find an explicit analytical expression of the detection probability for any number of input photons, any number of on/off detectors, and we include quantum efficiency and a false count probability. This allows us to explicitly invert the conditional probability using Bayes' theorem and express the number of photons that we had at the input in the most unbiased way possible with ready-to-use formulas. We conclude with some examples.
Single-photon detectors are widely used in modern quantum optics experiments and applications. Like all detectors, it is important for these devices to be accurately calibrated. A single-photon detector is calibrated by determining its detection efficiency; the common method to measure this quantity requires comparison to another detector. Here, we suggest a method to measure the detection efficiency of a single-photon detector without requiring an external reference detector. Our method is valid for individual single-photon detectors as well as multiplexed detectors, which are known to be photon number resolving. The method exploits the even-number photon-statistics of a nonlinear source, as well as the nonlinear loss of a single-photon detector that occurs when multiple photons are incident simultaneously. We have analytically modeled multiplexed detectors and used the results to experimentally demonstrate the calibration of a single-photon detector without the need for an external reference detector.
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.
We present a scheme for non-deterministically approximating photon number resolving detectors using non-discriminating detectors. The model is simple in construction and employs very few physical resources. Despite its non-determinism, the proposal may nonetheless be suitable for use in some quantum optics experiments in which non-determinism can be tolerated. We analyse the detection scheme in the context of an optical implementation of the controlled-NOT gate, an inherently non-deterministic device. This allows the gate's success probability to be traded away for improved gate fidelity, assuming high efficiency detectors. The scheme is compared to two other proposals, both deterministic, for approximating discriminating detectors using non-discriminating detectors: the cascade and time division multiplexing schemes.
Photon number resolving detectors are the ultimate measurement of quantum optics, which is the reason why developing the technology is getting significant attention in recent years. With this arises the question of how to evaluate the performance of the detectors. We suggest that performance of a photon number detector can be evaluated by comparing it to a multiplex of on-off detectors in a practical scenario: conditional preparation of a photon number state. Here, both the quality of the prepared state and the probability of the preparation are limited by the number of on-off detectors in the multiplex, which allows us to set benchmarks that can be achieved or surpassed by the photon number resolving detectors.
We analyze the performance of photon-number-resolving (PNR) detectors and introduce a figure of merit for the accuracy of such detectors. This figure of merit is the (worst-case) probability that the photon-number-resolving detector correctly predicts the input photon number. Simulations of various PNR detectors based on multiplexed single-photon ``click detectors'' is performed. We conclude that the required quantum efficiency is very high in order to achieve even moderate (up to a handful) photon resolution, we derive the required quantum efficiency as a function of the the maximal photon number one wants to resolve, and we show that the number of click detectors required grows quadratically with the maximal number of photons resolvable.