2006/11/30 by J. Řeháček, Jaroslav Rehacek, Z. Hradil +4 · 8 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Convergence (economics) #Direct-conversion receiver #Expectation–maximization algorithm #Homodyne detection #Iterative method #Mathematical optimization #Mathematics #Maximization #Maximum likelihood #Optics #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum state #Quantum tomography #Rate of convergence #Statistics #Telecommunications #Tomography #quant-ph
paper · pdf · doi:10.1103/physreva.75.042108
published as Physical Review A 75, 042108 (2007) · v2: Convergence proof added
arxiv created 2007/02/22 · openalex publication_date 2007/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements. The algorithm is characterized by a very high convergence rate and features a simple adaptive procedure that ensures likelihood increase in every iteration and convergence to the maximum-likelihood state. We apply the algorithm to homodyne tomography of optical states and quantum tomography of entangled spin states of trapped ions and investigate its convergence properties.