Related papers: Conditional Effects, Observables and Instruments
In the context of having an instrumental variable, the standard practice in causal inference begins by targeting an effect of interest and proceeds by formulating assumptions enabling its identification. We turn this around by adhering to…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
In this paper we consider finite conditional random quantities and conditional previsions assessments in the setting of coherence. We use a suitable representation for conditional random quantities; in particular the indicator of a…
The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction…
The histories-based framework of Quantum Measure Theory assigns a generalized probability or measure $\mu(E)$ to every (suitably regular) set $E$ of histories. Even though $\mu(E)$ cannot in general be interpreted as the expectation value…
Quantum operations are used to describe the observed probability distributions and conditional states of the measured system. In this paper, we address the problem of their joint measurability (coexistence). We derive two equivalent…
Every theory of information, including classical and quantum, can be studied in the framework of operational probabilistic theories--where the notion of test generalizes that of quantum instrument, namely a collection of quantum operations…
In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lueders - von Neumann measurement to…
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for…
A simple model of quantum particle is proposed in which the particle in a {\it macroscopic} rest frame is represented by a {\it microscopic d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The state vectors are…
Given a normalized state-vector $\psi $, we define the conditional expectation $\mathbb{E }_{\psi } (A | B ) $ of a Hermitian operator $A $ with respect to a strongly commuting family of self-adjoint operators $B $ as the best…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is…
The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here,…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
Conditioning is a key feature in probabilistic programming to enable modeling the influence of data (also known as observations) to the probability distribution described by such programs. Determining the posterior distribution is also…
In the following we revisit the frequency interpretation of probability of Richard von Mises, in order to bring the essential implicit notions in focus. Following von Mises, we argue that probability can only be defined for events that can…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…