Related papers: The Quantum Bayes Rule and Generalizations from th…
The fundamentals of the Maximum Entropy principle as a rule for assigning and updating probabilities are revisited. The Shannon-Jaynes relative entropy is vindicated as the optimal criterion for use with an updating rule. A constructive…
Probabilistic reasoning systems combine different probabilistic rules and probabilistic facts to arrive at the desired probability values of consequences. In this paper we describe the MESA-algorithm (Maximum Entropy by Simulated Annealing)…
Quantum state tomography is an integral part of quantum computation and offers the starting point for the validation of various quantum devices. One of the central tasks in the field of state tomography is to reconstruct with high fidelity,…
The objective of Bayesian inference is often to infer, from data, a probability measure for a random variable that can be used as input for Monte Carlo simulation. When datasets for Bayesian inference are small, a principle challenge is…
In this paper, we discuss the connection between two genuinely quantum phenomena --- the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
A transition matrix can be constructed through the partial contraction of two given quantum states. We analyze and compare four different definitions of entropy for transition matrices, including (modified) pseudo entropy, SVD entropy, and…
Several different uncertain inference systems (UISs) have been developed for representing uncertainty in rule-based expert systems. Some of these, such as Mycin's Certainty Factors, Prospector, and Bayes' Networks were designed as…
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty…
The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…
Quantum scale estimation, as introduced and explored here, establishes the most precise framework for the estimation of scale parameters that is allowed by the laws of quantum mechanics. This addresses an important gap in quantum metrology,…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
Standard quantum mechanics is an idealisation based on infinite-precision objects: point states, exact probabilities, and sharp measurements. Yet every real experiment has finite resolution, and for macroscopic systems we never have access…
Generalized measures of quantum correlations are derived by taking Bayes' rule as the only fundamental principle. The resulting quantifiers satisfy several desirable conditions for a measure of quantum correlations and are shown to admit…
The maximum entropy principle (MEP) apparently allows us to derive, or justify, fundamental results of equilibrium statistical mechanics. Because of this, a school of thought considers the MEP as a powerful and elegant way to make…
We give some results relating asymptotic characterisations of maximum entropy probability measures to characterisations of Bayes optimal classifiers. Our main theorems show that maximum entropy is a universally Bayes optimal decision rule…
Entanglement-enhanced quantum metrology explores the utilization of quantum entanglement to enhance measurement precision. When particles in a probe are prepared into a quantum entangled state, they collectively accumulate information about…
The uncertainty principle, which bounds the uncertainties involved in obtaining precise outcomes for two complementary variables defining a quantum particle, is a crucial aspect in quantum mechanics. Recently, the uncertainty principle in…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
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…