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Quantum interference and Bayes theorem

Filippo Neri

This note is a comment on the "quantum interferometry" section of Reference [1]. It points out that the methods of that section can be applied to more general states than the ones that are discussed in Ref. [1].

arXiv:quant-ph/0601061Jan 10, 20060 citations

Quantum Theory of Jaynes' Principle, Bayes' Theorem, and Information

Hermann Haken

WORLD SCIENTIFIC eBooksDec 9, 20140 citations

Quantum State Reduction and the Quantum Bayes Principle

Masanao Ozawa

arXiv:quant-ph/9705030Springer eBooksJan 1, 199718 citations

Bayes' theorem and quantum retrodiction

Stephen Mark Barnett, David Thomas Pegg, John Jeffers

We derive on the basis of Bayes' theorem a simple but general expression for the retrodicted premeasurement state associated with the result of any measurement. The retrodictive density operator is the normalized probability operator measure element associated with the result. We examine applications to quantum optical cryptography and to the optical beam splitter.

arXiv:quant-ph/0106139Journal of Modern OpticsSep 1, 200074 citations

Does the uncertainty relation determine the quantum state?

Olga V. Man’ko, Vladimir I. Man’ko, Giuseppe Marmo +2 more

arXiv:quant-ph/0604044Physics Letters AMay 23, 200625 citations

State retrieval beyond Bayes' retrodiction

Jacopo Surace, Matteo Scandi

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.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.

arXiv:2201.09899QuantumApr 27, 202322 citations

Is Bayes Theorem Applicable to all Quantum States?

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