Related papers: The Quantum Bayes Rule and Generalizations from th…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this letter, we introduce a systematic method to construct a series of entropies,…
The uncertainty principle bounds the uncertainties about incompatible measurements, clearly setting quantum theory apart from the classical world. Its mathematical formulation via uncertainty relations, plays an irreplaceable role in…
Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum…
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…
Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic interpretation.…
In quantum information geometry, the curvature of von-Neumann entropy and relative entropy induce a natural metric on the space of mixed quantum states. Here we use this information metric to construct a random matrix ensemble for states…
This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
Using the monotonity of relative entropy of composite quantum systems we obtain new entropic inequalities for arbitrary density matrices of single qudit states. Example of qutrit state inequalities and the "qubit portrait" bound for the…
The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose,…
Quantum embedding methods have become a powerful tool to overcome deficiencies of traditional quantum modelling in materials science. However, while these are systematically improvable in principle, in practice it is rarely possible to…
The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…
Quantum metrology offers an enhanced performance in experiments such as gravitational wave-detection, magnetometry or atomic clocks frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features…
The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical…
(Jaynes') Method of (Shannon-Kullback's) Relative Entropy Maximization (REM or MaxEnt) can be - at least in the discrete case - according to the Maximum Probability Theorem (MPT) viewed as an asymptotic instance of the Maximum Probability…
The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…
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…
Whenever we do not have an informationally complete set of measurements, the estimate of a quantum state can not be uniquely determined. In this case, among the density matrices compatible with the available data, it is commonly preferred…
We point out a general framework that encompasses most cases in which quantum effects enable an increase in precision when estimating a parameter (quantum metrology). The typical quantum precision-enhancement is of the order of the square…