Critical reflections on quantum probability theory

László E. Szabó

pp. 201-219

in: John von Neumann and the foundations of quantum physics, Berlin, Springer, 2001

Abstract

The story of quantum probability theory and quantum logic begins with von Neumann's recognition¹, that quantum mechanics can be regarded as a kind of "probability theory", if the subspace lattice L(H) of the system's Hilbert space H plays the role of event algebra and the "tr(WE)'-s play the role of probability distributions over these events. This idea had been completed in the Gleason theorem ²: