Related papers: The Quantum Bayes Rule and Generalizations from th…
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…
We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
In this thesis we start by providing some detail regarding how we arrived at our present understanding of probabilities and how we manipulate them - the product and addition rules by Cox. We also discuss the modern view of entropy and how…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes the pragmatic elements in the derivation. An epistemic notion of information is defined in…
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a…
We show that Skilling's method of induction leads to a unique general theory of inductive inference, the method of Maximum relative Entropy (ME). The main tool for updating probabilities is the logarithmic relative entropy; other entropies…
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first…
Entropy maximization procedure has been a general practice in many diverse fields of science to obtain the concomitant probability distributions. The consistent use of the maximization procedure on the other hand requires the probability…
Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy,…
We introduce two methods for estimating the density matrix for a quantum system: Quantum Maximum Likelihood and Quantum Variational Inference. In these methods, we construct a variational family to model the density matrix of a mixed…
Quantum computation has been growing rapidly in both theory and experiments. In particular, quantum computing devices with a large number of qubits have been developed by IBM, Google, IonQ, and others. The current quantum computing devices…
Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…
It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…