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

Annual Meeting Optical Society of America

Homodyne statistics

Samuel L. Braunstein

Published Jan 1, 1990• 0 citations
Publisher

Abstract

The balanced homodyne detector is the paradigm of phase-sensitive detection schemes in quantum optics. We study the effects of a quantum local oscillator in a coherent state for this detector when it is coupled to a single signal mode. We calculate explicit general expressions for the output statistics of the difference current of this detector (applicable even to non-classical states), and compare them to the statistics of the so-called quadrature-phase amplitude. We show that the naive condition that the number of quanta in the local oscillator be much larger than the number in the signal is not sufficient to ensure that the homodyne detector approximates an ideal detectorof the quadrature-phase amplitude, further, we derive explicit conditions for this approximation to be achieved when the signal is a coherent state or a superposition of coherent states.

DOI
10.1364/oam.1990.tunn5

Related papers

Homodyne statistics

Samuel L. Braunstein

It is usually assumed that a balanced homodyne detector measures a variable called the quadrature phase amplitude of a signal field. We examine this assumption by obtaining analytic expressions for the probability statistics for the output of such a detector for a single-mode signal with both signal and local oscillator treated quantum mechanically. We investigate the conditions under which the statistics of the quadrature phase are reproduced in the actual output of the detector. We show that the most obvious condition---that the number of quanta in the local oscillator be much larger than the number in the signal---is not sufficient to ensure that a balanced homodyne detector acts like an ideal detector of quadrature phases. Furthermore, we obtain the explicit conditions that are necessary and sufficient to reproduce the interference features in the homodyne statistics of a superposition of coherent states.

Physical Review A•Jul 1, 1990•80 citations

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

Statistics of difference events in homodyne detection

W. Vogel, Jens Grabow

The statistics of the difference events in a balanced homodyne-detection scheme is studied without using the standard assumption of a strong, classical local oscillator. Starting from the quantum theory of photon counting, we derive the probability distribution for the difference events in the two detection channels. In the limit of the local oscillator being strong compared with the signal, the difference-number statistics tends to the statistics of the electric-field strength of the signal field. For weak signals, this limit may be obtained already far from a classical behavior of the local oscillator. While changing the local oscillator intensity, a transition of the observable concerning the signal field occurs from the photon-number difference towards the electric-field strength. Such a measurement scheme renders it possible to observe the quantum features of a coherent state or a single-photon state from the point of view of the field-strength statistics, a picture which is closely related to classical optics. The possibility to get some insight in the statistical properties of the phase difference of two microscopic fields is discussed.

Physical Review A•May 1, 1993•90 citations

Full statistics of ideal homodyne detection using real (noisy) local oscillator

A. Auyuanet, Eugenia Benech, H. Failache +1 more

We show that the full statistics of the outputs of two detectors in a balanced homodyne detection setup involving a local oscillator in an ideal coherent state are experimentally accessible despite the excess noise existing in actual laser sources. This possibility is illustrated using phase randomized coherent states’ signals from which the statistics of Fock states can accurately be obtained. The experimental verification of the recently predicted [Phys. Rev. A98, 013832 (2018)PLRAAN1050-294710.1103/PhysRevA.98.013832] two-detector correlation probability for Fock states |1⟩ and |2⟩ is presented.

arXiv:1808.02753•Journal of the Optical Society of America B•Dec 18, 2018•3 citations

Eight-port homodyne detector: The effect of imperfections on quantum random-number generation and on detection of quadratures

Alberto Barchielli, Alberto Santamato

The eight-port homodyne detector is an optical circuit designed to perform the monitoring of two quadratures of an optical field: the signal. By using quantum Bose fields and quantum stochastic calculus, we give a complete quantum description of this apparatus, when used as quadrature detector in continuous time. We can treat either the traveling waves in the optical circuit or the observables involved in the detection part: two couples of photodiodes, postprocessing of the output currents\dots{}. The analysis includes imperfections, such as not perfectly balanced beam splitters, detector efficiency, electronic noise, phase and intensity noise in the laser acting as local oscillator; this last noise is modeled by using mixtures of field coherent states as statistical operator of the laser component. Due to the monitoring in continuous time, the output is a stochastic process and its full probability distribution is obtained. When the output process is sampled at discrete times, the quantum description can be reduced to discrete mode operators, but at the price of having random operators, which contain also the noise of the local oscillator. Consequently, the local oscillator noise has a very different effect on the detection results with respect to an additive noise, such as the noise in the electronic components. As an application, the problem of secure random-number generation is considered, based on the local oscillator shot noise. The rate of random bits that can be generated is quantified by the min-entropy; the possibility of classical and quantum side information is taken into account by suitable conditional min-entropies. The final rate depends on which parts of the apparatus are considered to be secure and on which ones are considered to be exposed to the intervention of an intruder. In some experimentally realistic situations, the entropy losses are computed, depending on the values of the parameters quantifying the imperfections.

arXiv:2204.10616•Physical Review A•Aug 30, 2022•2 citations

Design and simulation of a 300 MHz Balanced Homodyne Detector for quantum photonics

Jiayi Yang

Balanced Homodyne Detection (BHD), introduced in the 1970s, enables highly sensitive detection of phase and amplitude variations in weak light. Initially developed as an advanced optical detection technique, it rapidly became essential in quantum optics for accurately quantifying quadrature components and detecting squeezed states at the shot-noise limit. Today, BHD plays a critical role in diverse fields such as high-precision quantum metrology, gigabit speed optical communications, gravitational wave detection, and large-scale quantum information systems. In this study, a BHD simulation was implemented with a 90 phase difference between the local oscillator and the signal, thus enabling the extraction of the phase quadratureP^component of the optical field.

Advances in Engineering Innovation•Jul 10, 2025•0 citations
The balanced homodyne detector is the paradigm of phase-sensitive detection schemes in quantum optics. We study the effects of a quantum local oscillator in a coherent state for this detector when it is coupled to a single signal mode. We calculate explicit general expressions for the output statistics of the difference current of this detector (applicable even to non-classical states), and compare them to the statistics of the so-called quadrature-phase amplitude. We show that the naive condition that the number of quanta in the local oscillator be much larger than the number in the signal is not sufficient to ensure that the homodyne detector approximates an ideal detectorof the quadrature-phase amplitude, further, we derive explicit conditions for this approximation to be achieved when the signal is a coherent state or a superposition of coherent states.
It is usually assumed that a balanced homodyne detector measures a variable called the quadrature phase amplitude of a signal field. We examine this assumption by obtaining analytic expressions for the probability statistics for the output of such a detector for a single-mode signal with both signal and local oscillator treated quantum mechanically. We investigate the conditions under which the statistics of the quadrature phase are reproduced in the actual output of the detector. We show that the most obvious condition---that the number of quanta in the local oscillator be much larger than the number in the signal---is not sufficient to ensure that a balanced homodyne detector acts like an ideal detector of quadrature phases. Furthermore, we obtain the explicit conditions that are necessary and sufficient to reproduce the interference features in the homodyne statistics of a superposition of coherent states.
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.
The statistics of the difference events in a balanced homodyne-detection scheme is studied without using the standard assumption of a strong, classical local oscillator. Starting from the quantum theory of photon counting, we derive the probability distribution for the difference events in the two detection channels. In the limit of the local oscillator being strong compared with the signal, the difference-number statistics tends to the statistics of the electric-field strength of the signal field. For weak signals, this limit may be obtained already far from a classical behavior of the local oscillator. While changing the local oscillator intensity, a transition of the observable concerning the signal field occurs from the photon-number difference towards the electric-field strength. Such a measurement scheme renders it possible to observe the quantum features of a coherent state or a single-photon state from the point of view of the field-strength statistics, a picture which is closely related to classical optics. The possibility to get some insight in the statistical properties of the phase difference of two microscopic fields is discussed.
We show that the full statistics of the outputs of two detectors in a balanced homodyne detection setup involving a local oscillator in an ideal coherent state are experimentally accessible despite the excess noise existing in actual laser sources. This possibility is illustrated using phase randomized coherent states’ signals from which the statistics of Fock states can accurately be obtained. The experimental verification of the recently predicted [Phys. Rev. A98, 013832 (2018)PLRAAN1050-294710.1103/PhysRevA.98.013832] two-detector correlation probability for Fock states |1⟩ and |2⟩ is presented.
The eight-port homodyne detector is an optical circuit designed to perform the monitoring of two quadratures of an optical field: the signal. By using quantum Bose fields and quantum stochastic calculus, we give a complete quantum description of this apparatus, when used as quadrature detector in continuous time. We can treat either the traveling waves in the optical circuit or the observables involved in the detection part: two couples of photodiodes, postprocessing of the output currents\dots{}. The analysis includes imperfections, such as not perfectly balanced beam splitters, detector efficiency, electronic noise, phase and intensity noise in the laser acting as local oscillator; this last noise is modeled by using mixtures of field coherent states as statistical operator of the laser component. Due to the monitoring in continuous time, the output is a stochastic process and its full probability distribution is obtained. When the output process is sampled at discrete times, the quantum description can be reduced to discrete mode operators, but at the price of having random operators, which contain also the noise of the local oscillator. Consequently, the local oscillator noise has a very different effect on the detection results with respect to an additive noise, such as the noise in the electronic components. As an application, the problem of secure random-number generation is considered, based on the local oscillator shot noise. The rate of random bits that can be generated is quantified by the min-entropy; the possibility of classical and quantum side information is taken into account by suitable conditional min-entropies. The final rate depends on which parts of the apparatus are considered to be secure and on which ones are considered to be exposed to the intervention of an intruder. In some experimentally realistic situations, the entropy losses are computed, depending on the values of the parameters quantifying the imperfections.
Balanced Homodyne Detection (BHD), introduced in the 1970s, enables highly sensitive detection of phase and amplitude variations in weak light. Initially developed as an advanced optical detection technique, it rapidly became essential in quantum optics for accurately quantifying quadrature components and detecting squeezed states at the shot-noise limit. Today, BHD plays a critical role in diverse fields such as high-precision quantum metrology, gigabit speed optical communications, gravitational wave detection, and large-scale quantum information systems. In this study, a BHD simulation was implemented with a 90 phase difference between the local oscillator and the signal, thus enabling the extraction of the phase quadratureP^component of the optical field.