Maximum-Likelihood Quantum State Tomography by Cover's Method with Non-Asymptotic Analysis

• URL: http://arxiv.org/abs/2110.00747v1
• Date: Sat, 2 Oct 2021 08:03:13 GMT
• Title: Maximum-Likelihood Quantum State Tomography by Cover's Method with Non-Asymptotic Analysis
• Authors: Chien-Ming Lin and Hao-Chung Cheng and Yen-Huan Li
• Abstract summary: We propose an iterative algorithm that computes the maximum-likelihood estimate in quantum state tomography. The per-iteration computational complexity of the algorithm is $O ( D 3 + N D 2 )$, where $N$ denotes the number of measurement outcomes.
• Score: 10.758021887982782
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose an iterative algorithm that computes the maximum-likelihood estimate in quantum state tomography. The optimization error of the algorithm converges to zero at an $O ( ( 1 / k ) \log D )$ rate, where $k$ denotes the number of iterations and $D$ denotes the dimension of the quantum state. The per-iteration computational complexity of the algorithm is $O ( D ^ 3 + N D ^2 )$, where $N$ denotes the number of measurement outcomes. The algorithm can be considered as a parameter-free correction of the $R \rho R$ method [A. I. Lvovsky. Iterative maximum-likelihood reconstruction in quantum homodyne tomography. \textit{J. Opt. B: Quantum Semiclass. Opt.} 2004] [G. Molina-Terriza et al. Triggered qutrits for quantum communication protocols. \textit{Phys. Rev. Lett.} 2004.].

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