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

International Conference on Quantum Information

Tomography for quantum diagnostics

Jaroslav Řeháček, Dmitri S. Mogilevtsev, Z. Hradil

Published Jan 1, 2008• 0 citations
Publisher

Abstract

We introduce a resolution measure, which provides error bars for any quantity inferred from tomographic measurement. Method is illustrated with the diagnostics of non-classical behavior using Wigner function at the origin.
DOI
10.1364/icqi.2008.qwb1

Related papers

Tomography for quantum diagnostics

Jaroslav Řeháček, Dmitri S. Mogilevtsev, Z. Hradil

The quantification of relevant statistical errors is an indispensable but often neglected part of any tomographic scheme used for quantum diagnostic purposes. We introduce a novel resolution measure, which provides 'error bars' for any inferred quantity of interest. This is illustrated with an example of the diagnostics of non-classical states based on the value of the reconstructed Wigner function at the origin of the phase space. We show that such diagnostics is meaningful only when a lot of prior information on the measured quantum state is available. Our resolution measure also provides an effective tool for optimization and resolution tuning of tomography schemes.

New Journal of Physics•Apr 14, 2008•57 citations

Quantum diagnosis of molecules: A method for measuring directly the Wigner function of a molecular vibrational state

L. Davidovich, Miguel Orszag, Nicim Zagury

We propose a method for measuring directly the Wigner function of a molecular vibrational state. Our method does not involve the calculation of integral transforms, as in tomographic proposals, and is applicable to a large class of molecular states.

Physical Review A•Apr 1, 1998•11 citations

What information about a wave function is given by “measuring” it with the help of the tomographic method of recovering the Wigner distribution?

Lev B. Klebanov, L. A. Khalfin

Journal of Mathematical Sciences•Feb 1, 1999•0 citations

Quantum tomographic reconstruction with error bars: a Kalman filter approach

Koenraad M R Audenaert, Stefan Scheel

We present a novel quantum tomographic reconstruction method based on Bayesian inference via the Kalman filter update equations. The method not only yields the maximum likelihood/optimal Bayesian reconstruction but also a covariance matrix expressing the measurement uncertainties in a complete way. From this covariance matrix the error bars on any derived quantity can be easily calculated. This is a first step towards the broader goal of devising an omnibus reconstruction method that could be adapted to any tomographic setup with little effort and that treats measurement uncertainties in a statistically well-founded way. In this first part, we restrict ourselves to the important subclass of tomography based on measurements with discrete outcomes (as opposed to continuous ones), and we also ignore any measurement imperfections (dark counts, less than unit detector efficiency, etc), which will be treated in a follow-up paper. We illustrate our general theory on real tomography experiments of quantum optical information processing elements.

arXiv:0809.3359•New Journal of Physics•Feb 13, 2009•36 citations

Quantum tomography of a molecular bond in ice

I. U. Goldschleger, Marie N. van Staveren, Vartkess Ara Apkarian

We present the moving picture of a molecular bond, in phase-space, in real-time, at resolution limited by quantum uncertainty. The images are tomographically reconstructed Wigner distribution functions (WDF) obtained from four-wave mixing measurements on Br2-doped ice. The WDF completely characterizes the dissipative quantum evolution of the system, which despite coupling to the environment retains quantum coherence, as evidenced by its persistent negative Wigner hole. The spectral decomposition of the WDF allows a direct visualization of wavefunctions and spatiotemporal coherences of the system and the system-bath interaction. The measurements vividly illustrate nonclassical wave mechanics in a many-body system, in ordinary condensed matter.

The Journal of Chemical Physics•Jul 17, 2013•10 citations

Direct measurement of the Wigner function by photon-number-resolving detection

Niranjan Sridhar, Reihaneh Shahrokhshahi, Aaron Miller +4 more

We extended the seminal experiment of Banaszek et al. of quantum tomography by photon counting without Radon transform postprocessing to the more general case of photon fluxes with more than one photon per detection time.

•Jan 1, 2015•1 citation
The quantification of relevant statistical errors is an indispensable but often neglected part of any tomographic scheme used for quantum diagnostic purposes. We introduce a novel resolution measure, which provides 'error bars' for any inferred quantity of interest. This is illustrated with an example of the diagnostics of non-classical states based on the value of the reconstructed Wigner function at the origin of the phase space. We show that such diagnostics is meaningful only when a lot of prior information on the measured quantum state is available. Our resolution measure also provides an effective tool for optimization and resolution tuning of tomography schemes.
We present a novel quantum tomographic reconstruction method based on Bayesian inference via the Kalman filter update equations. The method not only yields the maximum likelihood/optimal Bayesian reconstruction but also a covariance matrix expressing the measurement uncertainties in a complete way. From this covariance matrix the error bars on any derived quantity can be easily calculated. This is a first step towards the broader goal of devising an omnibus reconstruction method that could be adapted to any tomographic setup with little effort and that treats measurement uncertainties in a statistically well-founded way. In this first part, we restrict ourselves to the important subclass of tomography based on measurements with discrete outcomes (as opposed to continuous ones), and we also ignore any measurement imperfections (dark counts, less than unit detector efficiency, etc), which will be treated in a follow-up paper. We illustrate our general theory on real tomography experiments of quantum optical information processing elements.
We present the moving picture of a molecular bond, in phase-space, in real-time, at resolution limited by quantum uncertainty. The images are tomographically reconstructed Wigner distribution functions (WDF) obtained from four-wave mixing measurements on Br2-doped ice. The WDF completely characterizes the dissipative quantum evolution of the system, which despite coupling to the environment retains quantum coherence, as evidenced by its persistent negative Wigner hole. The spectral decomposition of the WDF allows a direct visualization of wavefunctions and spatiotemporal coherences of the system and the system-bath interaction. The measurements vividly illustrate nonclassical wave mechanics in a many-body system, in ordinary condensed matter.