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Quantum tomography

Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, Fernando G. S. L. Brandão

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.18154/rwth-2026-03965

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We show a sample of some relevant developments in classical and quantum tomography that have taken place over the last twenty years. We will present a general conceptual framework that provides a simple unifying mathematical picture for them and, as an effective use of it, three subjects have been chosen that offer a wide panorama of the scope of classical and quantum tomography: tomography along lines and submanifolds, coherent state tomography and tomography in the abstract algebraic setting of quantum systems.
Quantum state tomography provides a fundamental framework for reconstructing quantum states. When the measurement data are not informationally complete, the observed statistics admit multiple compatible density matrices, making the reconstruction problem inherently underdetermined and calling for the selection of a meaningful estimator. Two well-established approaches to address this ambiguity are Maximum Entropy (MaxEnt) and Variational Quantum Tomography (VQT). A variant of VQT, named VQT∞_\infty∞​, has been introduced to reproduce MaxEnt-like solutions. In this work, we generalize this approach by introducing a parametrized cost function that interpolates between the 1-norm and the infinity norm, thereby unifying VQT and VQT∞_\infty∞​ within a single framework. By tuning the associated hyperparameters, the proposed method enables controlled exploration of the set of compatible density matrices. We show that this interplay yields reconstructed states with higher fidelity to the MaxEnt solution than those obtained via VQT∞_\infty∞​ while preserving computational tractability.