A problem of information gain by quantal measurements

Herbert S. Green

I D Ivonovic

Under the assumption that every quantal measurement may give data about the post-measurement state of the inspected ensemble, the problem of the state determination is reconsidered. It is shown that orthogonal decomposition of the set of complex, n*n, Hermitian matrices into the commutative subsets allows operators to be found such that post-measurement information on these observables allows a partial (in some cases total) determination of the pre-measurement state to be effected.

T. F. Hill

The consistency problem of quantum mechanics may be resolved by regarding any measurement performed on an atomic system as essentially involving an interaction between the atomic system and a macroscopic measuring apparatus and the subsequent behaviour of the apparatus in producing a signal to indicate the result of the measurement. Of central importance in such an approach, therefore, is the study of large quantal systems. Along these lines, two approaches to the consistency problem have been provided; one, by the Italian group of Daneri, Loinger and Prosperi, based on a time-independent ergodic theory of large quantal systems; the other by the Belgian group of George, Prigogine and Rosenfeld, based on a time-dependent theory. In this thesis these two theories are compared and are shown to be equivalent.

J. C. G. Lesurf

Rafael D. Sorkin

In this paper we address the extension problem for quantal measures of path-integral type, concentrating on two cases: sequential growth of causal sets and a particle moving on the finite lattice ℤn. In both cases, the dynamics can be coded into a vector-valued measure μ on Ω, the space of all histories. Initially, μ is just defined on special subsets of Ω called cylinder events, and we would like to extend it to a larger family of subsets (events) in analogy to the way this is done in the classical theory of stochastic processes. Since quantally μ is generally not of bounded variation, a new method is required. We propose a method that defines the measure of an event by means of a sequence of simpler events that in a suitable sense converges to the event whose measure we are seeking to define. To this end, we introduce canonical sequences approximating certain events, and we propose a measure-based criterion for the convergence of such sequences. Applying the method, we encounter a simple event whose measure is zero classically but non-zero quantally.