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:2305.19397

Quantum State Characterization Using Measurement Configurations Inspired by Homodyne Detection

Arik Avagyan

Published May 30, 2023• 1 citation
arXivHTMLPDF

Abstract

In the standard homodyne configuration, an unknown optical state is combined with a local oscillator (LO) on a beam splitter (BS). Good quadrature measurements require a high-amplitude LO and two high-efficiency photodiodes whose signals are subtracted and normalized. By changing the LO phase, it is then possible to infer the optical state in the mode matching the LO. For quantum information processing, the states of interest are in well-separated modes, corresponding to a pulsed configuration with one relevant LO mode per measurement. We theoretically investigate what can be learned about the unknown optical state by counting photons in one or both outgoing paths after the BS, keeping the LO mode fixed but choosing its phase and magnitude. We consider measurement configurations where the BS acts differently on different sets of matching modes. When the BS acts identically on all matching modes it is possible to determine the content of the unknown optical state in the mode matching the LO conditional on each number of photons in the orthogonal modes on the same path. In particular, if both the phase and the intensity of the LO can be varied, then the statistics of just one of the counters is enough to infer these parameters, while in the case of an LO with fixed intensity both detectors are needed to accomplish this. Our results are derived by demonstrating a bijection, or lack thereof, between the probability distributions over the space of outcomes of the counter(s) and certain parameters of the unknown state for different measurement configuration. We report an experiment that was conducted to demonstrate the theory in the case where the BS acts differently depending on the polarization.

DOI
10.48550/arxiv.2305.19397

Related papers

Homodyne-like detection scheme based on photon-number-resolving detectors

Alessia Allevi, Matteo Bina, Stefano Olivares +1 more

Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.

International Journal of Quantum Information•Dec 1, 2017•13 citations

Kramers-Kronig detection in the quantum regime

Thomas Pousset, Maxime Federico, Romain Alléaume +1 more

We investigate the quantization of Kramers-Kronig detection technique initially developed for classical optical communications. It consists in mixing the unknown field with a strong monochromatic local oscillator on an unbalanced beam splitter. A single output of the beam splitter undergoes a direct detection of the optical intensity by means of a single photodiode. When the measured output verifies signal processing constraints, namely, the minimal phase and the single-sideband constraints, Kramers-Kronig detection reconstructs the phase of the signal from the intensity measurements via a digitally computed Hilbert transform. The local oscillator being known, Kramers-Kronig detection allows for reconstructing the quadratures of the unknown field. We show that this result holds in the quantum regime up to first order in the local oscillator amplitude and thus that Kramers-Kronig detection acts as a coherent detection able to measure both quadratures, making it a Gaussian measurement similar to double homodyne detection. We also study in detail the phase information measured by Kramers-Kronig detection for bosonic coherent states, monomode pure states, and mixed states. Finally, we propose and investigate a spectral tomography protocol for single-photon states that is inspired by Kramers-Kronig detection and relies on a spectral engineering of the single photon.

arXiv:2407.20827•Physical Review Research•Oct 7, 2025•0 citations

Characterizing photon number statistics using conjugate optical homodyne detection

Bing Qi, Pavel Lougovski, Brian P. Williams

We study the problem of determining the photon number statistics of an unknown quantum state using conjugate optical homodyne detection. We quantify the information gain in a single-shot measurement and show that the photon number statistics can be recovered in repeated measurements on an ensemble of identical input states without scanning the phase of the input state or randomizing the phase of the local oscillator used in homodyne detection. We demonstrate how the expectation maximization algorithm and Bayesian inference can be utilized to facilitate the reconstruction and illustrate our approach by conducting experiments to study the photon number distributions of a weak coherent state and a thermal state source.

arXiv:1702.02558•Optics Express•Jan 6, 2020•30 citations

Measurement of the Polarization State of a Weak Signal Field by Homodyne Detection

Sun-Hyun Youn

Information carried by an optical beam of light can usually be conveyed in the form of a temporal modulation of the intensity, phase, frequency or the polarization of the constituent mode(s). In that regard, homodyne detection is one of the most popular and standard method to measure the quantum mechanical properties of light Yuen & Shapiro (1978); Yuen et al. (1979); Yuen & Shapiro (1980); Yurke (1985). The quantum theory of homodyne detection originated principally from the works of Yuen and Shapiro et al. Yuen & Shapiro (1978); Yuen et al. (1979). In this method, a weak signal field is combined with a strong local oscillator field at a beam splitter, and the resulting signal is measured as a photocurrent. With the homodyne detection method, the quantum state of the signal field, such as the quadrature amplitude of the squeezed state, is easily measured Slusher et al. (1985); Wu et al. (1986 ); Polzik et al. (1992), and the quasiprobability distribution function can be measured by using the so-called optical homodyne tomography Smithey et al. (1993); Banaszek & W’odkiewicz (1996); Wallentowitz & Vogel (1996); Youn et al. (2001). Furthermore, optical homodyne detection is used to eavesdrop on the quantum key in quantum cryptography Hirano et al. (2000).

InTech eBooks•Mar 23, 2012•2 citations

Broadband pulsed quadrature measurements with calorimeters

Ezad Shojaee, James R. van Meter, Karl Mayer +2 more

A fundamental problem in quantum optics is to measure a quadrature operator of a mode described by a shape in the time or frequency domain. This can be done by pulsed homodyne detection, in which the signal and a high-amplitude pulsed local oscillator (LO) interfere on a beam splitter whose output ports are monitored by photodetectors. The quadrature value is proportional to the difference between the photodetectors' signals. When the shape of the mode is too broad in frequency, the lack of uniform spectral response of detectors prevents direct application of this technique. We show that pulsed homodyne detection can be generalized to broadband pulsed (BBP) homodyne detection with detectors such as calorimeters that detect total energy instead of total photon number. This generalization has applications in measurements of femtosecond pulses and, speculatively, of Rindler modes. We analyze how the implemented measurement approaches an ideal quadrature measurement with growing LO amplitude, and we prove that the moments of the measurement converge to the moments of the quadrature and that the measurement distributions converge weakly.

arXiv:2503.00188•Physical Review A•Oct 20, 2025•0 citations

In situ characterization of a photon-subtraction device via heralding counts and homodyne detection

Priyanka Sharma, Matteo G. A. Paris, Stefano Olivares

Photon subtraction is one of the most important techniques for generating non-Gaussian optical states and constitutes a key resource for quantum information processing and quantum metrology. The practical performance of a photon-subtraction device is primarily determined by the transmissivity of the beam splitter and the quantum efficiency of the heralding detector. Accurate knowledge of these parameters is therefore essential for assessing the quality of the generated non-classical states. In this work, we propose an experimentally feasible in situ scheme for the simultaneous estimation of these two parameters using only the measurement data produced during the operation of the device. Our protocol combines the click statistics of an on/off heralding detector with homodyne measurements performed on the transmitted mode of the beam splitter when fed by a displaced squeezed state. Within the framework of classical multi-parameter estimation theory, we derive the corresponding Fisher information matrix and investigate both joint and sequential estimation strategies. For simultaneous measurement of parameters, we evaluate the sloppiness of the underlying statistical model and analyze its dependence on the measured quadrature, probe photon number, squeezing fraction, beam splitter transmissivity, and detector efficiency. Our analysis proves that an appropriate choice of the homodyne quadrature substantially reduces parameter degeneracy and enables efficient simultaneous estimation. Furthermore, we show that the joint estimation strategy consistently provides a lower estimation bound than the sequential estimation approach over a broad range of experimentally relevant parameters.

quant-pharXiv:2609.10100•Sep 10, 2026•0 citations
In the standard homodyne configuration, an unknown optical state is combined with a local oscillator (LO) on a beam splitter (BS). Good quadrature measurements require a high-amplitude LO and two high-efficiency photodiodes whose signals are subtracted and normalized. By changing the LO phase, it is then possible to infer the optical state in the mode matching the LO. For quantum information processing, the states of interest are in well-separated modes, corresponding to a pulsed configuration with one relevant LO mode per measurement. We theoretically investigate what can be learned about the unknown optical state by counting photons in one or both outgoing paths after the BS, keeping the LO mode fixed but choosing its phase and magnitude. We consider measurement configurations where the BS acts differently on different sets of matching modes. When the BS acts identically on all matching modes it is possible to determine the content of the unknown optical state in the mode matching the LO conditional on each number of photons in the orthogonal modes on the same path. In particular, if both the phase and the intensity of the LO can be varied, then the statistics of just one of the counters is enough to infer these parameters, while in the case of an LO with fixed intensity both detectors are needed to accomplish this. Our results are derived by demonstrating a bijection, or lack thereof, between the probability distributions over the space of outcomes of the counter(s) and certain parameters of the unknown state for different measurement configuration. We report an experiment that was conducted to demonstrate the theory in the case where the BS acts differently depending on the polarization.
Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.
We investigate the quantization of Kramers-Kronig detection technique initially developed for classical optical communications. It consists in mixing the unknown field with a strong monochromatic local oscillator on an unbalanced beam splitter. A single output of the beam splitter undergoes a direct detection of the optical intensity by means of a single photodiode. When the measured output verifies signal processing constraints, namely, the minimal phase and the single-sideband constraints, Kramers-Kronig detection reconstructs the phase of the signal from the intensity measurements via a digitally computed Hilbert transform. The local oscillator being known, Kramers-Kronig detection allows for reconstructing the quadratures of the unknown field. We show that this result holds in the quantum regime up to first order in the local oscillator amplitude and thus that Kramers-Kronig detection acts as a coherent detection able to measure both quadratures, making it a Gaussian measurement similar to double homodyne detection. We also study in detail the phase information measured by Kramers-Kronig detection for bosonic coherent states, monomode pure states, and mixed states. Finally, we propose and investigate a spectral tomography protocol for single-photon states that is inspired by Kramers-Kronig detection and relies on a spectral engineering of the single photon.
We study the problem of determining the photon number statistics of an unknown quantum state using conjugate optical homodyne detection. We quantify the information gain in a single-shot measurement and show that the photon number statistics can be recovered in repeated measurements on an ensemble of identical input states without scanning the phase of the input state or randomizing the phase of the local oscillator used in homodyne detection. We demonstrate how the expectation maximization algorithm and Bayesian inference can be utilized to facilitate the reconstruction and illustrate our approach by conducting experiments to study the photon number distributions of a weak coherent state and a thermal state source.
Information carried by an optical beam of light can usually be conveyed in the form of a temporal modulation of the intensity, phase, frequency or the polarization of the constituent mode(s). In that regard, homodyne detection is one of the most popular and standard method to measure the quantum mechanical properties of light Yuen & Shapiro (1978); Yuen et al. (1979); Yuen & Shapiro (1980); Yurke (1985). The quantum theory of homodyne detection originated principally from the works of Yuen and Shapiro et al. Yuen & Shapiro (1978); Yuen et al. (1979). In this method, a weak signal field is combined with a strong local oscillator field at a beam splitter, and the resulting signal is measured as a photocurrent. With the homodyne detection method, the quantum state of the signal field, such as the quadrature amplitude of the squeezed state, is easily measured Slusher et al. (1985); Wu et al. (1986 ); Polzik et al. (1992), and the quasiprobability distribution function can be measured by using the so-called optical homodyne tomography Smithey et al. (1993); Banaszek & W’odkiewicz (1996); Wallentowitz & Vogel (1996); Youn et al. (2001). Furthermore, optical homodyne detection is used to eavesdrop on the quantum key in quantum cryptography Hirano et al. (2000).
A fundamental problem in quantum optics is to measure a quadrature operator of a mode described by a shape in the time or frequency domain. This can be done by pulsed homodyne detection, in which the signal and a high-amplitude pulsed local oscillator (LO) interfere on a beam splitter whose output ports are monitored by photodetectors. The quadrature value is proportional to the difference between the photodetectors' signals. When the shape of the mode is too broad in frequency, the lack of uniform spectral response of detectors prevents direct application of this technique. We show that pulsed homodyne detection can be generalized to broadband pulsed (BBP) homodyne detection with detectors such as calorimeters that detect total energy instead of total photon number. This generalization has applications in measurements of femtosecond pulses and, speculatively, of Rindler modes. We analyze how the implemented measurement approaches an ideal quadrature measurement with growing LO amplitude, and we prove that the moments of the measurement converge to the moments of the quadrature and that the measurement distributions converge weakly.
Photon subtraction is one of the most important techniques for generating non-Gaussian optical states and constitutes a key resource for quantum information processing and quantum metrology. The practical performance of a photon-subtraction device is primarily determined by the transmissivity of the beam splitter and the quantum efficiency of the heralding detector. Accurate knowledge of these parameters is therefore essential for assessing the quality of the generated non-classical states. In this work, we propose an experimentally feasible in situ scheme for the simultaneous estimation of these two parameters using only the measurement data produced during the operation of the device. Our protocol combines the click statistics of an on/off heralding detector with homodyne measurements performed on the transmitted mode of the beam splitter when fed by a displaced squeezed state. Within the framework of classical multi-parameter estimation theory, we derive the corresponding Fisher information matrix and investigate both joint and sequential estimation strategies. For simultaneous measurement of parameters, we evaluate the sloppiness of the underlying statistical model and analyze its dependence on the measured quadrature, probe photon number, squeezing fraction, beam splitter transmissivity, and detector efficiency. Our analysis proves that an appropriate choice of the homodyne quadrature substantially reduces parameter degeneracy and enables efficient simultaneous estimation. Furthermore, we show that the joint estimation strategy consistently provides a lower estimation bound than the sequential estimation approach over a broad range of experimentally relevant parameters.