Related papers: Probabilism for Stochastic Theories

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

One of the fundamental features of quantum mechanics is the superposition principle, a manifestation of which is embodied in quantum coherence. Coherence of a quantum state is invariably defined with respect to a preferred set of pointer…

It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle.…

In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…

In a recent paper Kent has pointed out that in consistent histories quantum theory it is possible, given initial and final states, to construct two different consistent families of histories, in each of which there is a proposition that can…

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…

We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…

Belief systems are often treated as globally consistent sets of propositions or as scalar-valued probability distributions. Such representations tend to obscure the internal structure of belief, conflate external credibility with internal…

Quantum entanglement and nonlocality are inequivalent notions: There exist entangled states that nevertheless admit local-realistic interpretations. This paper studies a special class of local-hidden-variable theories, in which the linear…

We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…

I start from the fundamental principles of non-relativistic quantum mechanics, without probability, and interpret them using the notion of coexistence: a quantum state can be read, not uniquely, as a coexistence of other quantum states,…

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…

Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about…

We use the probability of error as a measure of distinguishability between two pure and two mixed symmetric coherent states in the context of continuous variable quantum cryptography. We show that the two mixed symmetric coherent states (in…

I think we can agree that dealing with uncertainty is not easy. Probability is the main tool for dealing with uncertainty, and we know there are many probability-related puzzles and paradoxes. Here I describe a rather idiosyncratic…

In the present article we use the quantum formalism to describe the effects of risk and ambiguity in decision theory. The main idea is that the probabilities in the classic theory of expected utility are estimated probabilities, and thus do…

Standard rational expectations models with an occasionally binding zero lower bound constraint either admit no solutions (incoherence) or multiple solutions (incompleteness). This paper shows that deviations from full-information rational…

Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…

How should we model an observer within quantum mechanics or quantum field theory? How can classical physics emerge from a quantum model, and why should classical probability be useful? How can we model a selective measurement entirely…

We investigate the generic aspects of quantum coherence guided by the concentration of measure phenomenon. We find the average relative entropy of coherence of pure quantum states sampled randomly from the uniform Haar measure and show that…