Related papers: Conditional Effects, Observables and Instruments
This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The…
In this paper, a quantitative measure of partial observability is defined for PDEs. The quantity is proved to be consistent if the PDE is approximated using well-posed approximation schemes. A first order approximation of an unobservability…
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…
We consider the problem of defining conditional objects (a|b), which would allow one to regard the conditional probability Pr(a|b) as a probability of a well-defined event rather than as a shorthand for Pr(ab)/Pr(b). The next issue is to…
This article points out that observables and instruments can be combined in many ways that have natural and physical interpretations. We shall mainly concentrate on the mathematical properties of these combinations. Section~1 reviews the…
Our aim is to make a step towards clarification of foundations for the notion of entanglement (both physical and mathematical) by representing it in the conditional probability framework. In Schr\"odinger's words, this is entanglement of…
Sequential measurements of non-commuting observables produce order effects that are well-known in quantum physics. But their conceptual basis, a significant measurement interaction, is relevant for far more general situations. We argue that…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
A normalized positive operator measure $X\mapsto E(X)$ has the norm-1-property if $\no{E(X)}=1$ whenever $E(X)\ne O$. This property reflects the fact that the measurement outcome probabilities for the values of such observables can be made…
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…
We propose a general construction of an observable measuring the time of occurence of an effect in quantum theory. Time delay in potential scattering is computed as a straightforward application.
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…
We analyze the properties of the conditional amplitude operator, the quantum analog of the conditional probability which has been introduced in [quant-ph/9512022]. The spectrum of the conditional operator characterizing a quantum bipartite…
We describe a quantum mechanical measurement as a variational principle including interaction between the system under measurement and the measurement apparatus. Augmenting the action with a nonlocal term (a double integration over the…
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…
In a causal graphical model, an instrument for a variable X and its effect Y is a random variable that is a cause of X and independent of all the causes of Y except X. (Pearl (1995), Spirtes et al (2000)). Instrumental variables can be used…
Recent developments in the formalisation of quantum causal structures have made it possible to test and compare hypotheses about causal structure empirically, rather than being a-priori assumptions. Such differences in causal structure may…