Related papers: Quantum inferring acausal structures and the Monty…
We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
In this work we first propose to exploit the fundamental properties of quantum physics to evaluate the probability of events with projection measurements. Next, to study what events can be specified by quantum methods, we introduce the…
It is argued that the nature of probability is essentially informational rather than physical and that quantum mechanical predictions should be viewed as logical inferences made on the basis of the information content of a given…
Modern machine learning (ML) methods typically fail to adequately capture causal information. Consequently, such models do not handle data distributional shifts, are vulnerable to adversarial examples, and often learn spurious correlations.…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
We introduce a notion of strategies based on averaging for nonlocal games in quantum information theory. These so-called statistical strategies come in a commuting type and a more specific spatial type, which are respectively special cases…
Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for…
The main goal of this paper is to give a pedagogical introduction to Quantum Information Theory-to do this in a new way, using network diagrams called Quantum Bayesian Nets. A lesser goal of the paper is to propose a few new ideas, such as…
Complex information-processing systems, for example quantum circuits, cryptographic protocols, or multi-player games, are naturally described as networks composed of more basic information-processing systems. A modular analysis of such…
Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions --…
In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as…
We study quantum causal inference in a set-up proposed by Ried et al. [Nat. Phys. 11, 414 (2015)] in which a common-cause scenario can be mixed with a cause-effect scenario, and for which it was found that quantum mechanics can bring an…
In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard Hilbert space model of quantum…
Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the…
Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences…
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…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
The characterization of physical systems relies on the observable properties which are measured, and how such measurements are performed. Here we analyze two ways of assigning a description to a quantum system assuming that we only have…