The de Finetti theorem for test spaces

Details The de Finetti theorem for test spaces The de Finetti theorem for test spaces

2007-12-14

arxiv.org/abs/0712.2265v3

New J. Phys. 11, 033024 (2009)

Physics

Quantum Physics

10 pages, 3 figures, revtex4

Scientific paper

We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.

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