2015/09/30 by Christopher Granade, Joshua Combes, David G. Cory +1 · 107 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Bayesian inference #Bayesian probability #Computation #Computer science #Estimator #Gaussian Processes and Bayesian Inference #Mathematics #Optics #Physics #Prior probability #Quantum #Quantum mechanics #Quantum state #Quantum tomography #Range (aeronautics) #Statistical Mechanics and Entropy #Statistical physics #Statistics #Target Tracking and Data Fusion in Sensor Networks #Tomography #physics.data-an #quant-ph #stat.AP
paper · pdf · doi:10.1088/1367-2630/18/3/033024
published in New Journal of Physics 18(3), 033024 (IOP Publishing) · 25 pages, quite a lot of figures, two videos, a tutorial, and a partridge in a pear tree
openalex publication_date 2016/03/15 · arxiv created 2016/05/11 · arxiv updated 2016/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we address all three problems. First, we use modern statistical methods, as pioneered by Huszár and Houlsby (2012 Phys. Rev. A 85 052120 ) and by Ferrie (2014 New J. Phys. 16 093035 ), to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first priors on quantum states and channels that allow for including useful experimental insight. Finally, we develop a method that allows tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.