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Minimum Relative Entropy for Quantum Estimation: Feasibility and General Solution [article]

Mattia Zorzi, Francesco Ticozzi, Augusto Ferrante
2013 arXiv   pre-print
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion.  ...  A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever necessary, to relax the constraints in order to allow for a physically admissible solution  ...  A quantum minimum relative entropy method for state estimation has been discussed in [21] , [24] , where approximate solutions to minimum relative entropy problems are provided: the estimates are shown  ... 
arXiv:1301.6658v1 fatcat:j5h4d3hgrfat3nxdghjqbjd7pi

Generalized maximum entropy estimation [article]

Tobias Sutter, David Sutter, Peyman Mohajerin Esfahani, John Lygeros
2019 arXiv   pre-print
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise.  ...  We further demonstrate how the presented scheme can be used for approximating the chemical master equation through the zero-information moment closure method, and for an approximate dynamic programming  ...  Acknowledgments The authors thank Andreas Milias-Argeitis for helpful discussions regarding the moment closure example. TS and JL acknowledge "SystemsX" under the grant "SignalX".  ... 
arXiv:1708.07311v3 fatcat:yhs77edtizel3jdduevvcba3bq

Exact and approximate solutions for the quantum minimum-Kullback-entropy estimation problem

Carlo Sparaciari, Stefano Olivares, Francesco Ticozzi, Matteo G. A. Paris
2014 Physical Review A. Atomic, Molecular, and Optical Physics  
The minimum Kullback entropy principle (mKE) is a useful tool to estimate quantum states and operations from incomplete data and prior information.  ...  In general, the solution of a mKE problem is analytically challenging and an approximate solution has been proposed and employed in different context.  ...  Acknowledgments This work has been supported by MIUR (project FIRB "LiCHIS" -RBFR10YQ3H) and the University of Padua (project "QuantumFuture").  ... 
doi:10.1103/physreva.89.042124 fatcat:jkvy4eiurfeo3p5ib26sj3i3ga

The tightness of multipartite coherence from spectrum estimation [article]

Qi-Ming Ding, Xiao-Xu Fang, He Lu
2021 arXiv   pre-print
Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence.  ...  Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems.  ...  ACKNOWLEDGMENTS We are grateful to anonymous referees for providing very useful comments on earlier versions of this manuscript.  ... 
arXiv:2104.12094v2 fatcat:hl6p6ktrqfbgxn3szv32sj4ohq

The Tightness of Multipartite Coherence from Spectrum Estimation

Qi-Ming Ding, Xiao-Xu Fang, He Lu
2021 Entropy  
Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence.  ...  Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems.  ...  On the experimental side, the realization is focused on the detection of relative entropy of coherence [43] , and its feasibility for other coherence measures has not been tested.  ... 
doi:10.3390/e23111519 pmid:34828217 pmcid:PMC8621860 fatcat:ihne5ddylrgxrjhdilsjhlcxxi

Studies on Point Estimators for Incomplete Tomography of Qutrits [article]

Jing Hao Chai
2015 arXiv   pre-print
The main content of the thesis focuses on various methods of estimation such as maximum entropy and average estimator and show that they are quite different.  ...  This is a Bachelor's thesis on point estimators for incomplete tomography of qutrits as of 2014, submitted to the National University of Singapore.  ...  measured by quantum relative entropy.  ... 
arXiv:1503.06521v1 fatcat:trgsdalhirgrpn4fo7iczonf4q

Numerical estimation of the relative entropy of entanglement

Yuriy Zinchenko, Shmuel Friedland, Gilad Gour
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
We propose a practical algorithm for the calculation of the relative entropy of entanglement (REE), defined as the minimum relative entropy between a state and the set of states with positive partial transpose  ...  In low dimensions the implementation of the algorithm in MATLAB provides an estimation for the REE with an absolute error smaller than 10 −3 .  ...  solution is found in 93 iterations with the reported approximate relative entropy value r = 0.1308... and |3/4 log 3  ... 
doi:10.1103/physreva.82.052336 fatcat:t3y6a7ppgfclln56pgkjqtnpbe

Minimax Quantum Tomography: Estimators and Relative Entropy Bounds

Christopher Ferrie, Robin Blume-Kohout
2016 Physical Review Letters  
A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk.  ...  This makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states.  ...  This freedom is often removed in quantum problems by choosing the best or worst possible measurement (e.g., as in the definition of quantum relative entropy as the classical relative entropy of the most  ... 
doi:10.1103/physrevlett.116.090407 pmid:26991163 fatcat:acl2imrgkjaufbqjpzidh67fmq

Quantum Semiparametric Estimation [article]

Mankei Tsang, Francesco Albarelli, Animesh Datta
2020 arXiv   pre-print
Here we propose a theory of quantum semiparametric estimation that can circumvent both challenges and produce simple analytic bounds for a class of problems in which the dimensions are arbitrarily high  ...  Potential applications include quantum state characterization for many-body systems, optical imaging, and interferometry, where full tomography of the quantum state is often infeasible and only a few select  ...  Górecki, and J. Suzuki for useful discussions. This research is partly supported by the National Research Foundation (NRF) Singapore, under its Quantum Engineering Programme (Award QEP-P7). AD and FA  ... 
arXiv:1906.09871v6 fatcat:yx7s4tpndjbq3oxunkdnzvpume

Classification of motor imagery by means of cortical current density estimation and Von Neumann entropy

Baharan Kamousi, Ali Nasiri Amini, Bin He
2007 Journal of Neural Engineering  
The goal of the present study is to employ the source imaging methods such as cortical current density estimation for the classification of left-and right-hand motor imagery tasks, which may be used for  ...  Cortical current density distributions of left and right trials were classified from each other by exploiting the concept of Von Neumann entropy.  ...  Acknowledgments The authors are grateful to Zhongming Liu for useful discussions.  ... 
doi:10.1088/1741-2560/4/2/002 pmid:17409476 fatcat:zgoxtj25pneujgzylglef6vcq4

Time and spectral domain relative entropy: A new approach to multivariate spectral estimation [article]

Augusto Ferrante, Chiara Masiero, Michele Pavon
2011 arXiv   pre-print
The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes.  ...  Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy rates.  ...  Finally, in Section IX, we introduce the spectral relative entropy rate of Gaussian processes and establish a profound connection between time and spectral domain relative entropy rates. II.  ... 
arXiv:1103.5602v2 fatcat:ujqzl2rwybgalam3kwzemvilpe

Quantum Semiparametric Estimation

Mankei Tsang, Francesco Albarelli, Animesh Datta
2020 Physical Review X  
Here, we propose a theory of quantum semiparametric estimation that can circumvent both challenges and produce simple analytic bounds for a class of problems in which the dimensions are arbitrarily high  ...  Potential applications include quantum state characterization for many-body systems, optical imaging, and interferometry, where full tomography of the quantum state is often infeasible and only a few select  ...  Genoni both for several fruitful discussions and for making us aware of Ref. [35] . We are grateful to R. Nair, M. Guţă, R. Gill  ... 
doi:10.1103/physrevx.10.031023 fatcat:sc2gxlhj3bfpdgwvwozinygvmy

Device-independent randomness generation from several Bell estimators

Olmo Nieto-Silleras, Cédric Bamps, Jonathan Silman, Stefano Pironio
2018 New Journal of Physics  
Device-independent randomness generation and quantum key distribution protocols rely on a fundamental relation between the non-locality of quantum theory and its random character.  ...  We introduce protocols for device-independent randomness generation, secure against classical side information, that rely on the estimation of an arbitrary number of Bell expressions or even directly on  ...  our manuscript and for their useful comments.  ... 
doi:10.1088/1367-2630/aaaa06 fatcat:3am5nhr6pjdjvlbigllqkcplbe

Quantum Probability Estimation for Randomness with Quantum Side Information [article]

Emanuel Knill, Yanbao Zhang, Honghao Fu
2020 arXiv   pre-print
This leads to conditional min-entropy estimates for randomness generation.  ...  We develop a quantum version of the probability estimation framework [arXiv:1709.06159] for randomness generation with quantum side information.  ...  ACKNOWLEDGMENTS We thank Carl Miller and Peter Bierhorst for stimulating discussions, help with moving this project forward and editorial help.  ... 
arXiv:1806.04553v3 fatcat:i5lpgdfqgbc2poaycx4cahtjli

MELE: Maximum Entropy Leuven Estimators

Quirino Paris
2001 Social Science Research Network  
The generalized maximum entropy (GME) estimator of Golan, Judge and Miller depends upon subjective exogenous information that affects the estimated parameters in an unpredictable way.  ...  The ridge estimator is not generally accepted as a vital alternative to the ordinary least-squares (OLS) estimator because it depends upon unknown parameters.  ...  Golan, Judge and Miller present a thorough discussion of the Generalized Maximum Entropy (GME) estimator. Let = Zp, with p km ≥ 0 and p km m ∑ = 1 for k = 1,...,K .  ... 
doi:10.2139/ssrn.280304 fatcat:eexs3xoz4bd4dllenqjqu2dcne
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