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Entropy 2018, 20(8), 609; https://doi.org/10.3390/e20080609

Information Geometry of Randomized Quantum State Tomography

1
Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan
2
Graduate School of Informatics and Engineering, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan
*
Author to whom correspondence should be addressed.
Received: 29 June 2018 / Revised: 5 August 2018 / Accepted: 13 August 2018 / Published: 16 August 2018
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
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Abstract

Suppose that a d-dimensional Hilbert space H C d admits a full set of mutually unbiased bases | 1 ( a ) , , | d ( a ) , where a = 1 , , d + 1 . A randomized quantum state tomography is a scheme for estimating an unknown quantum state on H through iterative applications of measurements M ( a ) = | 1 ( a ) 1 ( a ) | , , | d ( a ) d ( a ) | for a = 1 , , d + 1 , where the numbers of applications of these measurements are random variables. We show that the space of the resulting probability distributions enjoys a mutually orthogonal dualistic foliation structure, which provides us with a simple geometrical insight into the maximum likelihood method for the quantum state tomography. View Full-Text
Keywords: quantum state tomography; mutually unbiased bases; information geometry; dualistic foliation; mixed coordinate system quantum state tomography; mutually unbiased bases; information geometry; dualistic foliation; mixed coordinate system
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Fujiwara, A.; Yamagata, K. Information Geometry of Randomized Quantum State Tomography. Entropy 2018, 20, 609.

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