Related papers: Quantum Probability and Decision Theory, Revisited
We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
I argue that the Oxford school Everett interpretation is internally incoherent, because we cannot claim that in an Everettian universe the kinds of reasoning we have used to arrive at our beliefs about quantum mechanics would lead us to…
Busch's theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleason's theorem. Here we show that a further generalisation is possible by reducing the number of quantum postulates used by Busch.…
The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.
We live in a world brimming with uncertainty, where we constantly have to make a lot of decisions under incomplete information. We are firm believers that our subjective belief cannot be computed by rigorous mathematical formula; instead…
We pose and solve a problem concerning consistent assignment of quantum probabilities to a set of bases associated with maximal projective measurements. We show that our solution is optimal. We also consider some consequences of the main…
Deutsch, Feynman, and Manin viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a…
Classical probability theory is based on assumptions which are often violated in practice. Therefore quantum probability is a proposed alternative not only in quantum physics, but also in other sciences. However, so far it mostly criticizes…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We…
Does the notion of a quantum randomized or nondeterministic algorithm make sense, and if so, does quantum randomness or nondeterminism add power? Although reasonable quantum random sources do not add computational power, the discussion of…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach…
If the quantum mechanical description of reality is not complete and a hidden variable theory is possible, what arises is the problem to explain where the rates of the outcomes of statistical experiments come from, as already noticed by…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
Within Bohm`s interpretation of quantum mechanics particles follow classical trajectories that are determined by the full solution of the time dependent Schroedinger equation. If this interpretation is consistent it must be possible to…
Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum…