State retrieval beyond Bayes' retrodiction

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.

References in corpus (8)

• Quantum Operation Time Reversal
• Quantum marginal problem and representations of the symmetric group
• Quantum Dynamics as an analog of Conditional Probability
• Fluctuation theorems from Bayesian retrodiction
• A non-commutative Bayes' theorem
• Entropic Updating of Probability and Density Matrices
• Thermodynamic Reverse Bounds for General Open Quantum Processes
• Lüders' and quantum Jeffrey's rules as entropic projections

Cited by in corpus (12)

• From time-reversal symmetry to quantum Bayes' rules
• Axioms for retrodiction: achieving time-reversal symmetry with a prior
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times
• Characterizing (non-)Markovianity through Fisher Information
• Quantum Bayes' rule and Petz transpose map from the minimum change principle
• Role of Dilations in Reversing Physical Processes: Tabletop Reversibility and Generalized Thermal Operations
• Petz recovery maps for qudit quantum channels
• A Retrodictive Approach to Quantum State Smoothing
• Proper and improper mixed states serve as different prior beliefs for quantum state retrodiction
• Tabletop reversibility of phase-covariant operations
• Universality and classification of elementary thermal operations
• Realizing the Petz Recovery Map on an NMR Quantum Processor