Improving Accuracy of Estimating Two-Qubit States with Hedged Maximum Likelihood

As a widely used reconstruction algorithm in quantum state tomography, maximum likelihood estimation tends to assign a rank-deficient matrix, which decreases estimation accuracy for certain quantum states. Fortunately, hedged maximum likelihood estimation （HMLE） [Phys. Rev. Lett. 105 （2010）200504] w...

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Published inChinese physics letters Vol. 34; no. 3; pp. 1 - 5
Main Author 殷琪 项国勇 李传锋 郭光灿
Format Journal Article
LanguageEnglish
Published 01.03.2017
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ISSN0256-307X
1741-3540
DOI10.1088/0256-307X/34/3/030301

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Abstract As a widely used reconstruction algorithm in quantum state tomography, maximum likelihood estimation tends to assign a rank-deficient matrix, which decreases estimation accuracy for certain quantum states. Fortunately, hedged maximum likelihood estimation （HMLE） [Phys. Rev. Lett. 105 （2010）200504] was proposed to avoid this problem. Here we study more details about this proposal in the two-qubit case and further improve its performance. We ameliorate the HMLE method by updating the hedging function based on the purity of the estimated state. Both performances of HMLE and ameliorated HMLE are demonstrated by numerical simulation and experimental implementation on the Werner states of polarization-entangled photons.
AbstractList As a widely used reconstruction algorithm in quantum state tomography, maximum likelihood estimation tends to assign a rank-deficient matrix, which decreases estimation accuracy for certain quantum states. Fortunately, hedged maximum likelihood estimation （HMLE） [Phys. Rev. Lett. 105 （2010）200504] was proposed to avoid this problem. Here we study more details about this proposal in the two-qubit case and further improve its performance. We ameliorate the HMLE method by updating the hedging function based on the purity of the estimated state. Both performances of HMLE and ameliorated HMLE are demonstrated by numerical simulation and experimental implementation on the Werner states of polarization-entangled photons.
Author 殷琪 项国勇 李传锋 郭光灿
AuthorAffiliation Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026 Synergetic Innovation Center of Quantum Information and Quantum Physics,University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026
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Notes 11-1959/O4
As a widely used reconstruction algorithm in quantum state tomography, maximum likelihood estimation tends to assign a rank-deficient matrix, which decreases estimation accuracy for certain quantum states. Fortunately, hedged maximum likelihood estimation （HMLE） [Phys. Rev. Lett. 105 （2010）200504] was proposed to avoid this problem. Here we study more details about this proposal in the two-qubit case and further improve its performance. We ameliorate the HMLE method by updating the hedging function based on the purity of the estimated state. Both performances of HMLE and ameliorated HMLE are demonstrated by numerical simulation and experimental implementation on the Werner states of polarization-entangled photons.
Qi Yin 1,2, Guo-Yong Xiang 1,2, Chuan-Feng Li 1,2, Guang-Can Guo1,2 （1Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026 2 Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026）
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