An operational approach to quantum probability

@article{Davies1970AnOA,
  title={An operational approach to quantum probability},
  author={E. B. Davies and John T. Lewis},
  journal={Communications in Mathematical Physics},
  year={1970},
  volume={17},
  pages={239-260}
}
In order to provide a mathmatical framework for the process of making repeated measurements on continuous observables in a statistical system we make a mathematical definition of an instrument, a concept which generalises that of an observable and that of an operation. It is then possible to develop such notions as joint and conditional probabilities without any of the commutation conditions needed in the approach via observables. One of the crucial notions is that of repeatability which we… 

Reconstruction theorem for a quantum stochastic process

This paper gives a physically interpretable--in real time--definition of a QSP as families of representations of the observable algebra 'B' in a common (large) system by indicating a universal method

The operational approach to algebraic quantum theory I

Recent work of Davies and Lewis has suggested a mathematical framework in which the notion of repeated measurements on statistical physical systems can be examined. This paper is concerned with an

QUANTUM STOCHASTIC PROCESSES.

. In order to describe rigorously certain measurement procedures, where observations of the arrival of quanta at a counter are made throughout an interval of time, it is necessary to introduce the

Quantum stochastic processes

In order to describe rigorously certain measurement procedures, where observations of the arrival of quanta at a counter are made throughout an interval of time, it is necessary to introduce the

On the quantum theory of sequential measurements

The quantum theory of sequential measurements is worked out and is employed to provide an operational analysis of basic measurement theoretical notions such as coexistence, correlations,

A model of a quantum mechanical treatment of measurement with a physical interpretation

Projections onto minimum uncertainty states for Weyl systems are interpreted as being associated with elementary particles. This identification yields physically motivated definitions of

Quantum Mechanics and Operational Probability Theory

We discuss a generalization of the standard notion of probability space and show that the emerging framework, to be called operational probability theory, can be considered as underlying quantal

Hyperfinite-operational Approach to the Problem of Time Reversibility of Quantum Mechanics

This paper outlines a mathematical framework of quantum probability in which the time asymmetry in describing measuring processes is avoided. The main objects of the framework are hyperfinite

The Quantum Logical and the Operational Description for Physical Systems

In this talk we show how an operatonal description naturally arises from a Quantum Logical description. The mathematical support of this construction is the ordered vector space E consisting of the
...

References

SHOWING 1-10 OF 21 REFERENCES

Quantum stochastic processes

In order to describe rigorously certain measurement procedures, where observations of the arrival of quanta at a counter are made throughout an interval of time, it is necessary to introduce the

Measurement of Time Correlations in Quantum-Mechanical Systems.

TLDR
The use of such partial information to predict the results of subsequent measurements is studied, including the use of the autocorrelation function for a particle counter in a scattering experiment.

Probability in Physics and a Theorem on Simultaneous Observability

It is nearly thirty years since A. N. Kolmogorov explicitly wrote down the axioms of modern probability theory in his celebrated monograph [10]. During the intervening decades this theory has seen

Baser*-semigroups and the logic of quantum mechanics

The theory of orthomodular ortholattices provides mathematical constructs utilized in the quantum logic approach to the mathematical foundations of quantum physics. There exists a remarkable

CONDITIONAL EXPECTATION IN AN OPERATOR ALGEBRA, II

The theory of rings of operators of von Neumann has been developed by many authors, especially since it has been regarded as a non-commutative extension of the integration over a measure space by

Expectations in an operator algebra

(0. 5) 1* = 1 and will be called abelian if it satisfies moreover (0.6) (xy) = (jy#). Many known operations on C*-algebras can be considered as expections: EXAMPLE 1. If σ is a state (in the sense of

THE ALGEBRA OF MICROSCOPIC MEASUREMENT.

  • J. Schwinger
  • Biology
    Proceedings of the National Academy of Sciences of the United States of America
  • 1959
TLDR
1 Redfield, A. C., Amin, C. C, et al., in Buzzati-Traverso, A Symposium on Perspectives in Marine Biology (University of California Press, 1958).

Über die Zustandsänderung durch den Meßprozeß

Die statistische Transformationstheorie enthalt nicht nur Vorschriften fur die Berechnung von Meswahrscheinlichkeiten sondern bedarf zur Abrundung einer Aussage uber die Zustandsanderung durch den