Information Geometry of Randomized Quantum State Tomography
Department of Mathematics, Osaka University, Toyonaka, Osaka 560-0043, Japan
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
Suppose that a d
-dimensional Hilbert space
admits a full set of mutually unbiased bases
. A randomized quantum state tomography is a scheme for estimating an unknown quantum state on
through iterative applications of measurements
, 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.
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MDPI and ACS Style
Fujiwara, A.; Yamagata, K. Information Geometry of Randomized Quantum State Tomography. Entropy 2018, 20, 609.
Fujiwara A, Yamagata K. Information Geometry of Randomized Quantum State Tomography. Entropy. 2018; 20(8):609.
Fujiwara, Akio; Yamagata, Koichi. 2018. "Information Geometry of Randomized Quantum State Tomography." Entropy 20, no. 8: 609.
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