Related papers: Quantum Bayesian Inference in Quasiprobability Rep…
Bayes' rule connects forward and reverse processes in classical probability theory, and its quantum analogue has been discussed in terms of the Petz (transpose) map. For quantum dynamics governed by the Lindblad equation, the corresponding…
Bayes' rule $\mathbb{P}(B|A)\mathbb{P}(A)=\mathbb{P}(A|B)\mathbb{P}(B)$ is one of the simplest yet most profound, ubiquitous, and far-reaching results of classical probability theory, with applications in any field utilizing statistical…
Bayes' rule, which is routinely used to update beliefs based on new evidence, can be derived from a principle of minimum change. This principle states that updated beliefs must be consistent with new data, while deviating minimally from the…
We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
I describe a method of inferring the past of quantum observables given the initial state and the subsequent measurement results using Wigner quasi-probability representations. The method is proved to be compatible with logic for large…
We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs). This formulation provides a direct interpretation of density matrices as quasi-moment matrices. Using…
As a compact representation of joint probability distributions over a dependence graph of random variables, and a tool for modelling and reasoning in the presence of uncertainty, Bayesian networks are of great importance for artificial…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
In the Quantum-Bayesian interpretation of quantum theory (or QBism), the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In…
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
This paper shows how inference is treated within the context of Eigenlogic projection operators in linear algebra. In Eigenlogic operators represent logical connectives, their eigenvalues the truth-values and the associated eigenvectors the…
We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional…
There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with quantum channels. The result is a convex,…
Conditioning is a key feature in probabilistic programming to enable modeling the influence of data (also known as observations) to the probability distribution described by such programs. Determining the posterior distribution is also…
This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…