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PreprintarXiv licencearXiv

Connecting Quantum Tomography and Quantum Retrodiction

  • Sebastian Murk
  • Ian Tan
  • Fabian Müller
  • Dominik Šafránek
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Abstract

Quantum tomography and quantum retrodiction are traditionally viewed as separate inference tasks. We show that the two are manifestations of the same underlying principle. We prove that the Petz recovery map of a measurement channel is a gradient of the log-likelihood used in maximum-likelihood tomography, and we derive its extension to arbitrary quantum channels. Consequently, for measurement channels, repeated applications of the Petz map monotonically increase the likelihood, naturally yielding a method for quantum tomography.

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Cite

BibTeXRIS
BibTeX
@misc{murk2026connecting,
  title = {{Connecting Quantum Tomography and Quantum Retrodiction}},
  author = {Sebastian Murk and Ian Tan and Fabian Müller and Dominik Šafránek},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.23777},
  eprint = {2606.23777},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.23777},
}
RIS
TY  - UNPB
TI  - Connecting Quantum Tomography and Quantum Retrodiction
AU  - Sebastian Murk
AU  - Ian Tan
AU  - Fabian Müller
AU  - Dominik Šafránek
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2606.23777
UR  - https://arxiv.org/abs/2606.23777
AB  - Quantum tomography and quantum retrodiction are traditionally viewed as separate inference tasks. We show that the two are manifestations of the same underlying principle. We prove that the Petz recovery map of a measurement channel is a gradient of the log-likelihood used in maximum-likelihood tomography, and we derive its extension to arbitrary quantum channels. Consequently, for measurement channels, repeated applications of the Petz map monotonically increase the likelihood, naturally yielding a method for quantum tomography.
ER  -