Related papers: Quantum Bayes' rule and Petz transpose map from th…
We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact.…
The aim of this manuscript is to introduce the Bayesian minimum message length principle of inductive inference to a general statistical audience that may not be familiar with information theoretic statistics. We describe two key minimum…
Bayesian implementation concerns decision making problems when agents have incomplete information. This paper proposes that the traditional sufficient conditions for Bayesian implementation shall be amended by virtue of a quantum Bayesian…
A mixed quantum state can be taken as capturing an unspecified form of ignorance; or as describing the lack of knowledge about the true pure state of the system ("proper mixture"); or as arising from entanglement with another system that…
Using a diagrammatic reformulation of Bayes' theorem, we provide a necessary and sufficient condition for the existence of Bayesian inference in the setting of finite-dimensional $C^*$-algebras. In other words, we prove an analogue of…
We propose a simple abstract formalisation of the act of observation, in which the system and the observer are assumed to be in a pure state and their interaction deterministically changes the states such that the outcome can be read from…
We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias…
Classical reverse diffusion is generated by changing the drift at fixed noise. We show that the quantum version of this principle obeys an exact law with a sharp phase boundary. For Gaussian pure-loss dynamics -- the canonical model of…
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…
We formulate a quantum theory of the Universe based on Bayesian probability. In this theory, the probability of the Universe is not a frequency probability, which can be obtained by observing experimental results several times, but is a…
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
A brief review is given of the present state of an approach to consistency between basic quantum mechanics and a unique macroscopic reality, with no assumption of branching in the state of the universe. The main new idea consists in the…
We propose the principle, the law of statistical balance for basic physical observables, which specifies quantum statistical theory among all other statistical theories of measurements. It seems that this principle might play in quantum…
Importance sampling is used to approximate Bayes' rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and further investigates the required sample size for…
We provide a mechanism by which, from a background independent model with no quantum mechanics, quantum theory arises in the same limit in which spatial properties appear. Starting with an arbitrary abstract graph as the microscopic model…
The usual formulation of quantum theory is rather abstract. In recent work I have shown that we can, nevertheless, obtain quantum theory from five reasonable axioms. Four of these axioms are obviously consistent with both classical…
This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current…
We give a condensed and accessible summary of a recent derivation of quantum theory from information-theoretic principles, and use it to study the consequences of this and other reconstructions for our conceptual understanding of the…
The fact that redundant information does not update a rational belief implies that rational beliefs are updated using Bayes rule. In the framework of Hild (1998a), this is true under mild conditions for discrete, continuous, and arbitrary…
In a quantum-Bayesian take on quantum mechanics, 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 this paper, we argue…