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Reconstructing quantum states and expectations via dynamical tomography

Marco Peruzzo1,*, Tommaso Grigoletto1,†, and Francesco Ticozzi1,2,‡

  • *Contact author: marco.peruzzo@dei.unipd.it
  • †Contact author: tommaso.grigoletto@unipd.it
  • ‡Contact author: ticozzi@dei.unipd.it
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Phys. Rev. A 113, 032435 – Published 17 March, 2026

DOI: https://doi.org/10.1103/x88t-j8k9

Abstract

When the dynamics of a quantum system of interest is known, an informationally complete set of observables is not needed for state reconstruction via tomographic techniques: letting the system evolve before performing the measurement allows one to effectively extend the available ways to probe the system. This idea leads to dynamical quantum tomography, whose feasibility we characterize for general quantum dynamics using Krylov-based methods. Specializing in Markovian ones, we also provide deterministic tests and randomized ones to effectively assess parametric dynamics. The limits of the methods are explored by comparing unitary and open dynamics when a single observable is available, and the set of observables whose expectation can be reconstructed from the available ones characterized. The framework is illustrated with applications to a spin chain (with or without dissipation) and an electron-nuclear system.

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Phys. Rev. A 113, 032435– Published 17 March, 2026
  • Received 30 September 2025
  • Accepted 13 February 2026
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