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:1009.4054 · Physical Review A

Tilted phase-space measurements in the eight-port homodyne detection scheme

PEKKA J. LAHTI, Jussi Schultz

Published Nov 30, 2010• 0 citations
arXivHTMLPDF

Abstract

We show that the phase shift of $\frac{\ensuremath{\pi}}{2}$ is crucial for the phase-space translation covariance of the measured high-amplitude limit observable in eight-port homodyne detection. However, for an arbitrary phase shift $\ensuremath{\theta}$ we construct explicitly a different nonequivalent projective representation of ${\mathbb{R}}^{2}$ such that the observable is covariant with respect to this representation. As a result we are able to determine the measured observable for an arbitrary parameter field and phase shift. Geometrically the change in the phase shift corresponds to the tilting of one axis in the phase space of the system.

DOI
10.1103/physreva.82.052121

Related papers

Realistic eight-port homodyne detection and covariant phase space observables

PEKKA J. LAHTI, Juha-Pekka Pellonpää, Jussi Schultz

We consider the quantum optical eight-port homodyne detection scheme in the case that each of the associated photon detectors is assigned with a different quantum efficiency. We give a mathematically rigorous and strictly quantum mechanical proof of the fact that the measured observable (positive operator measure) in the high-amplitude limit is a smearing of the covariant phase space observable related to the ideal measurement, that is, the measurement performed with fully efficient detectors. The result is proved for an arbitary parameter field. Furthermore, we investigate some properties of the measured observable. In particular, we show that detector inefficiencies do not affect the observable's ability to distinguish between different states.

arXiv:1004.5006•Journal of Modern Optics•Jul 20, 2010•9 citations

A note on the measurement of phase space observables with an eight-port homodyne detector

Jukka Kiukas, PEKKA J. LAHTI

It is well known that the Husimi Q-function of the signal field can actually be measured by the eight-port homodyne detection technique, provided that the reference beam (used for homodyne detection) is a very strong coherent field so that it can be treated classically. Using recent rigorous results on the quantum theory of homodyne detection observables, we show that any phase space observable, and not only the Q-function, can be obtained as a high amplitude limit of the signal observable actually measured by an eight-port homodyne detector. The proof of this fact does not involve any classicality assumption.

arXiv:0708.4094•Journal of Modern Optics•Jul 1, 2008•21 citations

Operational theory of eight-port homodyne detection

Piotr Kochański, Krzysztof Wódkiewicz

The eight-port homodyne detection apparatus is analysed in the framework of the operational theory of quantum measurement. For an arbitrary quantum noise leaking through the unused port of the beam splitter, the positive operator valued measure and the corresponding operational homodyne observables are derived. It is shown that such an eight-port homodyne device can be used to construct the operational quantum trigonometry of an optical field. The quantum trigonometry and the corresponding phase space Wigner functions are derived for a signal field probed by a classical local oscillator and a squeezed vacuum in the unused port.

Journal of Modern Optics•Nov 1, 1997•4 citations

Operational Theory of the Eight-Port Homodyne Detection

Piotr Kochański, Krzysztof Wódkiewicz

The eight-port homodyne detection apparatus is analyzed in the framework of the operational theory of quantum measurement. For an arbitrary quantum noise leaking through the unused port of the beam splitter, the positive operator valued measure and the corresponding operational homodyne observables are derived. It is shown that such an eight-port homodyne device can be used to construct the operational quantum trigonometry of an optical field. The quantum trigonometry and the corresponding phase space Wigner functions are derived for a signal field probed by a classical local oscillator and a squeezed vacuum in the unused port.

arXiv:quant-ph/9611036•Nov 21, 1996•0 citations

Measuring the canonical phase with phase-space measurements

Juha-Pekka Pellonpää, Jussi Schultz

We study measurements of single-mode phase observables with emphasis on the canonical phase. We focus on the class of phase-shift covariant phase-space observables, which then yield the phase observables as the angle margins after integrating over the radial part. We consider the possibility of measuring such observables by using a double homodyne detector and its modification. We show that, in principle, the canonical phase distribution of the signal state can be measured via double homodyne detection by first processing the state using a two-mode unitary channel.

arXiv:1303.0127•Physical Review A•Jul 22, 2013•8 citations

Photon-counting, quantum-phase, and phase-space distributions

Matthias Freyberger, W. P. Schleich

We analyze a recent proposal for a new phase operator along with an eight-port homodyne detection experiment1 using phase-space functions. We show that the moments of these sine and cosine operators and, in particular, of the measured dispersion result from a phase distribution obtained from an appropriate Wigner function by integration over radius. We also connect this experiment with a different phase operator2 and the integrated Q-function.

Annual Meeting Optical Society of America•Jan 1, 1992•3 citations
We show that the phase shift of \ensuremathπ2\frac{\ensuremath{\pi}}{2}2\ensuremathπ​ is crucial for the phase-space translation covariance of the measured high-amplitude limit observable in eight-port homodyne detection. However, for an arbitrary phase shift \ensuremathθ\ensuremath{\theta}\ensuremathθ we construct explicitly a different nonequivalent projective representation of R2{\mathbb{R}}^{2}R2 such that the observable is covariant with respect to this representation. As a result we are able to determine the measured observable for an arbitrary parameter field and phase shift. Geometrically the change in the phase shift corresponds to the tilting of one axis in the phase space of the system.
We consider the quantum optical eight-port homodyne detection scheme in the case that each of the associated photon detectors is assigned with a different quantum efficiency. We give a mathematically rigorous and strictly quantum mechanical proof of the fact that the measured observable (positive operator measure) in the high-amplitude limit is a smearing of the covariant phase space observable related to the ideal measurement, that is, the measurement performed with fully efficient detectors. The result is proved for an arbitary parameter field. Furthermore, we investigate some properties of the measured observable. In particular, we show that detector inefficiencies do not affect the observable's ability to distinguish between different states.
It is well known that the Husimi Q-function of the signal field can actually be measured by the eight-port homodyne detection technique, provided that the reference beam (used for homodyne detection) is a very strong coherent field so that it can be treated classically. Using recent rigorous results on the quantum theory of homodyne detection observables, we show that any phase space observable, and not only the Q-function, can be obtained as a high amplitude limit of the signal observable actually measured by an eight-port homodyne detector. The proof of this fact does not involve any classicality assumption.
The eight-port homodyne detection apparatus is analysed in the framework of the operational theory of quantum measurement. For an arbitrary quantum noise leaking through the unused port of the beam splitter, the positive operator valued measure and the corresponding operational homodyne observables are derived. It is shown that such an eight-port homodyne device can be used to construct the operational quantum trigonometry of an optical field. The quantum trigonometry and the corresponding phase space Wigner functions are derived for a signal field probed by a classical local oscillator and a squeezed vacuum in the unused port.
The eight-port homodyne detection apparatus is analyzed in the framework of the operational theory of quantum measurement. For an arbitrary quantum noise leaking through the unused port of the beam splitter, the positive operator valued measure and the corresponding operational homodyne observables are derived. It is shown that such an eight-port homodyne device can be used to construct the operational quantum trigonometry of an optical field. The quantum trigonometry and the corresponding phase space Wigner functions are derived for a signal field probed by a classical local oscillator and a squeezed vacuum in the unused port.
We study measurements of single-mode phase observables with emphasis on the canonical phase. We focus on the class of phase-shift covariant phase-space observables, which then yield the phase observables as the angle margins after integrating over the radial part. We consider the possibility of measuring such observables by using a double homodyne detector and its modification. We show that, in principle, the canonical phase distribution of the signal state can be measured via double homodyne detection by first processing the state using a two-mode unitary channel.