State Retrieval Beyond Bayes’ Retrodiction

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Jacopo Surace and Matteo Scandi

ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), 08860, Spain

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Abstract

In the context of irreversible dynamics, associating to a physical process its intuitive reverse can result to be a quite ambiguous task. It is a standard choice to define the reverse process using Bayes’ theorem, but, in general, this choice is not optimal. In this work we explore whether it is possible to characterise an optimal reverse map building from the concept of state retrieval maps. In doing so, we propose a set of principles that state retrieval maps should satisfy. We find out that the Bayes inspired reverse is just one case in a whole class of possible choices, which can be optimised to give a map retrieving the initial state more precisely than the Bayes rule. Our analysis has the advantage of naturally extending to the quantum regime. In fact, we find a class of reverse transformations containing the Petz recovery map as a particular case, corroborating its interpretation as quantum analogue of the Bayes retrieval. Finally, we present numerical evidences that by adding a single extra axiom one can isolate the usual reverse process derived from Bayes’ theorem.

You can find our presentation State retrieval beyond Bayes’ retrodiction here.

► BibTeX data

@article{Surace2023stateretrieval, doi = {10.22331/q-2023-04-27-990}, url = {https://doi.org/10.22331/q-2023-04-27-990}, title = {State retrieval beyond {B}ayes’ retrodiction}, author = {Surace, Jacopo and Scandi, Matteo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {990}, month = apr, year = {2023}<br /> }

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Cited by

[1] Arthur J. Parzygnat and James Fullwood, “From time-reversal symmetry to quantum Bayes’ rules”, arXiv:2212.08088, (2022).

[2] Francesco Buscemi, Joseph Schindler, and Dominik Šafránek, “Observational entropy, coarse quantum states, and Petz recovery: information-theoretic properties and bounds”, arXiv:2209.03803, (2022).

[3] Paolo Abiuso, Matteo Scandi, Dario De Santis, and Jacopo Surace, “Characterizing (non-)Markovianity through Fisher Information”, arXiv:2204.04072, (2022).

[4] Arthur J. Parzygnat and Francesco Buscemi, “Axioms for retrodiction: achieving time-reversal symmetry with a prior”, arXiv:2210.13531, (2022).

[5] Akshaya Jayashankar and Prabha Mandayam, “Quantum Error Correction: Noise-adapted Techniques and Applications”, arXiv:2208.00365, (2022).

The above citations are from SAO/NASA ADS (last updated successfully 2023-04-29 01:39:52). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-04-29 01:39:51).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Time Stamp: April 27, 2023

Time Stamp: Sep 20, 2022

Qubit-efficient encoding schemes for binary optimisation problems

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Republished By Plato

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