Homodyning as Universal Detection

D’Ariano, Giacomo Mauro

doi:10.1007/978-1-4615-5923-8_27

Cited by 12 publications

(7 citation statements)

References 20 publications

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“…This is precisely the marginal distribution of the Wigner function of the state [14], that can thus be efficiently reconstructed [15]. This method has been shown to achieve the ultimate resolution predicted by the Fisher information [16], so it comes as no surprise that it is widely considered to be optimal in the CV community.The other technique, heterodyne detection [17][18][19][20][21][22][23][24][25][26][27], realizes the approximate measurement of two complementary orthogonal quadratures. This corresponds to a direct sampling of the Husimi Q function [28].…”

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confidence: 99%

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Evading Vacuum Noise: Wigner Projections or Husimi Samples?

et al. 2016

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The accuracy in determining the quantum state of a system depends on the type of measurement performed. Homodyne and heterodyne detection are the two main schemes in continuous-variable quantum information. The former leads to a direct reconstruction of the Wigner function of the state, whereas the latter samples its Husimi Q function. We experimentally demonstrate that heterodyne detection outperforms homodyne detection for almost all Gaussian states, the details of which depend on the squeezing strength and thermal noise.

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confidence: 99%

“…The other technique, heterodyne detection [17][18][19][20][21][22][23][24][25][26][27], realizes the approximate measurement of two complementary orthogonal quadratures. This corresponds to a direct sampling of the Husimi Q function [28].…”

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confidence: 99%

Evading Vacuum Noise: Wigner Projections or Husimi Samples?

et al. 2016

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“…Later the method of quantum homodyne tomography has been generalized to the estimation of an arbitrary observable of the field [29], with any number of modes [30], and, to arbitrary quantum systems via group theory [31], [32], [33], and with a general method for unbiasing noise [31], [32]. Eventually, it was recognized that the general data-processing is just an application of the theory of operator expansions [34], [35], which lead to identify quantum tomography as an informationally complete measurement [36]-a generalization of the concept of quorum of observables [12], [13].…”

Section: Historical Excursusmentioning

confidence: 99%

Optimal Quantum Tomography

Bisio

Chiribella

D’Ariano

et al. 2009

IEEE J. Select. Topics Quantum Electron.

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“…Recently, studies about the estimation of the unknown state are attracting many physicists [5,6,7,8]. Some of them were drawn by the variation of the measuring precision with respect to the number of samples of the unknown state [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…Thus early studies were lacking in asymptotic aspects, i.e. there were few researches with respect to reducing the estimation error by quantum correlations between samples.Recently, studies about the estimation of the unknown state are attracting many physicists [5,6,7,8]. Some of them were drawn by the variation of the measuring precision with respect to the number of samples of the unknown state [9,10].Nagaoka [11] studied, for the first time, asymptotic aspects of quantum estimation.…”

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Asymptotic Estimation Theory for a Finite-Dimensional Pure State Model

Hayashi¹

2005

Asymptotic Theory of Quantum Statistical Inference

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The optimization of measurement for n samples of pure sates are studied. The error of the optimal measurement for n samples is asymptotically compared with the one of the maximum likelihood estimators from n data given by the optimal measurement for one sample. IntroductionRecently, there has been a rise in the necessity for studies about statistical estimation for the unknown state, related to the corresponding advance in measuring technologies in quantum optics. An investigation including both quantum theory and mathematical statistics is necessary for an essential understanding of quantum theory because it has statistical aspects [1,2]. Therefore, it is indeed important to optimize the measuring process with respect to the estimation of the unknown state. Such research is known as quantum estimation, and was initiated by Helstrom in the late 1960s, originating in the optimization of the detecting process in optical communications [1]. In classical statistical estimation, one searches the most suitable estimator for which probability measure describes the objective probabilistic phenomenon. In quantum estimation, one searches the most suitable measurement for which density operator describes the objective quantum state.Contained among important results are three estimation problems. The first is of the complex amplitude of coherent light in thermal noise and the second is of the expectation parameters of quantum Gaussian state. The former was studied by Yuen and Lax [3] and the latter by Holevo [2]. These studies discovered that heterodyning is the most suitable for the estimation of the complex amplitude of coherent light in thermal noise. The third is a formulation of the covariant measurement with respect to an action of a group. It was studied by Holevo [2,4]. In the formulation, he established a quantum analogue of Hunt-Stein theorem.Quantum estimation, was first used in the evaluation of the estimation error of a single sample of the unknown state as it had advanced in connection with the optimization of the measuring process in optical communications. Thus early studies were lacking in asymptotic aspects, i.e. there were few researches with respect to reducing the estimation error by quantum correlations between samples.Recently, studies about the estimation of the unknown state are attracting many physicists [5,6,7,8]. Some of them were drawn by the variation of the measuring precision with respect to the number of samples of the unknown state [9,10].Nagaoka [11] studied, for the first time, asymptotic aspects of quantum estimation. He paid particular attention to the quantum correlations between samples of the unknown state, and studied the relation between the asymptotic estimation and the local detection of a one-parameter family of quantum states.In the early 1990s, Fujiwara and Nagaoka [12,13,14] studied the estimation problem for a multiparameter family consisting of pure states. They pioneered studies into the estimation problem of the complex amplitude of noiseless coherent light. The research f...

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Homodyning as Universal Detection

Cited by 12 publications

References 20 publications

Evading Vacuum Noise: Wigner Projections or Husimi Samples?

Evading Vacuum Noise: Wigner Projections or Husimi Samples?

Optimal Quantum Tomography

Asymptotic Estimation Theory for a Finite-Dimensional Pure State Model

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