相关论文: Quantum Probability Theory

Is is shown here that the "simple test of quantumness for a single system" of arXiv:0704.1962 (for a recent experimental realization see arXiv:0804.1646) has exactly the same relation to the discussion of to the problem of describing the…

We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels…

Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…

Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the latter always result from an…

It is argued that Feynman's rules for evaluating probabilities, combined with von Neumann's principle of psycho-physical parallelism, help avoid inconsistencies, often associated with quantum theory. The former allows one to assign…

The underlying probabilistic theory for quantum mechanics is non-Kolmogorovian. The order in which physical observables will be important if they are incompatible (non-commuting). In particular, the notion of conditioning needs to be…

Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is…

A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The…

Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…

An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…

Quantum randomness evidently transcends the classical framework of random variables defined on a single comprehensive Kolmogorov probability space. One prominent example is the quantum double-slit experiment due to Feynman (1951, 1966). A…

In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…

It is shown that the classical book by von Neumann proposing dynamics of measured systems with "reduction (or collapse) of system's wave packet" contains also hints how to avoid this discontinuity in time evolution of the measured system…

We give a tutorial exposition of the analogue of the filtering equation for quantum systems focusing on the quantum probabilistic framework and developing the ideas from the classical theory. Quantum covariances and conditional expectations…

A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…

Probabilistic models require the notion of event space for defining a probability measure. An event space has a probability measure which ensues the Kolmogorov axioms. However, the probabilities observed from distinct sources, such as that…

General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…

The primary motivation for Moyal's approach to quantum mechanics was to develop a phase space formalism for quantum phenomena by generalising the techniques of classical probability theory. To this end, Moyal introduced a quantum version of…

Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…

We survey the development of probability from 1900, starting with Bachelier's theory of speculation. Fisher information appears in the theory of estimation. We touch on Brownian motion, and the Wiener integral. The Ito calculus, and its…