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:quant-ph/9511017 · Physical Review A

Quantum state measurement by realistic heterodyne detection

Matteo G. A. Paris

Published Apr 1, 1996• 41 citations
arXivHTMLPDF

Abstract

The determination of the quantum properties of a single-mode radiation field by heterodyne or double homodyne detection is studied. The realistic case of not fully efficient photodetectors is considered. It is shown that a large amount of quite precise information is available, whereas the completeness of such information is also discussed. Some examples are given and the special case of states expressed as a finite superposition of number states is considered in some detail. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.53.2658

Related papers

Homodyning and heterodyning the quantum phase

Giacomo Mauro D’Ariano, Chiara Macchiavello, Matteo G. A. Paris

The double-homodyne and the heterodyne detection schemes for phase shifts between two synchronous modes of the electromagnetic field are analyzed in the framework of quantum estimation theory. The probability operator-valued measures (POM's) of the detectors are evaluated and compared with the ideal one in the limit of strong local reference oscillator. The present operational approach leads to a reasonable definition of phase measurement, whose sensitivity is actually related to the output r.m.s. noise of the photodetector. We emphasize that the simple-homodyne scheme does not correspond to a proper phase-shift measurements as it is just a zero-point detector. The sensitivity of all detection schemes are optimized at fixed energy with respect to the input state of radiation. It is shown that the optimal sensitivity can be actually achieved using suited squeezed states.

•May 1, 1994•0 citations

Unbalanced homodyning for quantum state measurements

Sascha Wallentowitz, W. Vogel

We propose the reconstruction of the quantum state of light from the homodyne photocounting statistics of a single, realistic photodetector. Contrary to the development of homodyning over the last decade, our approach is based on unbalanced detection with a weak local oscillator. Representing the quantum state in terms of s-parametrized quasiprobability distributions, the method even allows one to determine the Wigner function provided the quantum efficiency of the detector is sufficiently large. We show that perturbing effects due to classical noise of the local oscillator are small. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Jun 1, 1996•301 citations

Quantum-state homodyne measurement with vacuum ports

A. Zucchetti, W. Vogel, D.‐G. Welsch

We show that the quantum state of an N-mode light field can be reconstructed from the difference statistics recorded in multiport homodyning with N unused input ports. The theory is applied to balanced homodyne six-port detection, which is shown to be suited for measuring the Q function of a single-mode radiation field. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Jul 1, 1996•40 citations

Quantum Theory of Optical Homodyne and Heterodyne Detection

Matthew J. Collett, R. Loudon, Crispin W. Gardiner

The theory of balanced homodyne and heterodyne detection is developed for inputs in which the signal field is in an arbitrary quantum state and the local-oscillator field is in a highly excited coherent state. Exact expressions are derived for the photocount moment-generating functions in the special case of a coherent signal. For more general signals, the first two moments of the photocount probability distribution are determined. The moments are evaluated for the examples of a coherent signal with a chaotic noise component, and for squeezed light derived from a degenerate and from a non-degenerate parametric amplifier. The corresponding moments for direct detection are obtained so that comparisons can be made. The Kelley-Kleiner photocount distribution formula is adapted to balanced detection schemes. Light beams are characterized throughout by their energy fluxes, and the theory accordingly describes steady-state experiments.

Journal of Modern Optics•Jun 1, 1987•171 citations

Noise in homodyne and heterodyne detection

Horace P. Yuen, Vincent W. S. Chan

Quantum noise in optical heterodyning and homodyning, usually analyzed under the assumption that the photodetector output is conditionally Poisson,1,2 is frequently supposed to arise from local oscillator (LO) shot noise. However, a fully quantum mechanical analysis from Yuen and Shapiro3 has shown that it actually arises from the signal quantum fluctuation; in particular homodyning and heterodyning are realizations of abstract quantum measurements of the field quadratures. We analyze the effect of LO noise, both quantum and excess noise, on homodyne and heterodyne detection. For conventional input light, i.e., fields in coherent states or their random superpositions, we demonstrate how a conditionally Poisson calculation would yield the correct answer but incorrect interpretation for the detection quantum noise.

Conference on Lasers and Electro-Optics•Jan 1, 1983•13 citations

Two-mode quantum-optical state measurement: Sampling the joint density matrix

Michael G. Raymer, D. F. McAlister, Ulf Leonhardt

We propose schemes for measuring the joint quantum state of a two-mode optical field using balanced homodyne detection, thereby generalizing earlier single-mode schemes. We distinguish between two cases---the case where the two modes are spatially separable and the case where they are nonseparable. For each case we present a generalization of the direct sampling method of state reconstruction and point out that its advantages over inverse Radon methods are even greater here than in the single-mode case. In the case of two modes that cannot be separated we propose a scheme in which a single balanced homodyne detector is used for data collection. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Sep 1, 1996•76 citations
The determination of the quantum properties of a single-mode radiation field by heterodyne or double homodyne detection is studied. The realistic case of not fully efficient photodetectors is considered. It is shown that a large amount of quite precise information is available, whereas the completeness of such information is also discussed. Some examples are given and the special case of states expressed as a finite superposition of number states is considered in some detail. \textcopyright{} 1996 The American Physical Society.
The double-homodyne and the heterodyne detection schemes for phase shifts between two synchronous modes of the electromagnetic field are analyzed in the framework of quantum estimation theory. The probability operator-valued measures (POM's) of the detectors are evaluated and compared with the ideal one in the limit of strong local reference oscillator. The present operational approach leads to a reasonable definition of phase measurement, whose sensitivity is actually related to the output r.m.s. noise of the photodetector. We emphasize that the simple-homodyne scheme does not correspond to a proper phase-shift measurements as it is just a zero-point detector. The sensitivity of all detection schemes are optimized at fixed energy with respect to the input state of radiation. It is shown that the optimal sensitivity can be actually achieved using suited squeezed states.
We propose the reconstruction of the quantum state of light from the homodyne photocounting statistics of a single, realistic photodetector. Contrary to the development of homodyning over the last decade, our approach is based on unbalanced detection with a weak local oscillator. Representing the quantum state in terms of s-parametrized quasiprobability distributions, the method even allows one to determine the Wigner function provided the quantum efficiency of the detector is sufficiently large. We show that perturbing effects due to classical noise of the local oscillator are small. \textcopyright{} 1996 The American Physical Society.
The theory of balanced homodyne and heterodyne detection is developed for inputs in which the signal field is in an arbitrary quantum state and the local-oscillator field is in a highly excited coherent state. Exact expressions are derived for the photocount moment-generating functions in the special case of a coherent signal. For more general signals, the first two moments of the photocount probability distribution are determined. The moments are evaluated for the examples of a coherent signal with a chaotic noise component, and for squeezed light derived from a degenerate and from a non-degenerate parametric amplifier. The corresponding moments for direct detection are obtained so that comparisons can be made. The Kelley-Kleiner photocount distribution formula is adapted to balanced detection schemes. Light beams are characterized throughout by their energy fluxes, and the theory accordingly describes steady-state experiments.
Quantum noise in optical heterodyning and homodyning, usually analyzed under the assumption that the photodetector output is conditionally Poisson,1,2 is frequently supposed to arise from local oscillator (LO) shot noise. However, a fully quantum mechanical analysis from Yuen and Shapiro3 has shown that it actually arises from the signal quantum fluctuation; in particular homodyning and heterodyning are realizations of abstract quantum measurements of the field quadratures. We analyze the effect of LO noise, both quantum and excess noise, on homodyne and heterodyne detection. For conventional input light, i.e., fields in coherent states or their random superpositions, we demonstrate how a conditionally Poisson calculation would yield the correct answer but incorrect interpretation for the detection quantum noise.
We propose schemes for measuring the joint quantum state of a two-mode optical field using balanced homodyne detection, thereby generalizing earlier single-mode schemes. We distinguish between two cases---the case where the two modes are spatially separable and the case where they are nonseparable. For each case we present a generalization of the direct sampling method of state reconstruction and point out that its advantages over inverse Radon methods are even greater here than in the single-mode case. In the case of two modes that cannot be separated we propose a scheme in which a single balanced homodyne detector is used for data collection. \textcopyright{} 1996 The American Physical Society.