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| related topics |
| {observables, space, algebra} |
| {states, state, optimal} |
| {vol, operators, histories} |
| {particle, mechanics, theory} |
| {bell, inequality, local} |
| {let, theorem, proof} |
| {measurement, state, measurements} |
| {phase, path, phys} |
|
Quantum states and generalized observables: a simple proof of Gleason's
theorem
P. Busch
abstract: A quantum state can be understood in a loose sense as a map that assigns a
value to every observable. Formalizing this characterization of states in terms
of generalized probability distributions on the set of effects, we obtain a
simple proof of the result, analogous to Gleason's theorem, that any quantum
state is given by a density operator. As a corollary we obtain a von
Neumann-type argument against non-contextual hidden variables. It follows that
on an individual interpretation of quantum mechanics, the values of effects are
appropriately understood as propensities.
- oai_identifier:
- oai:arXiv.org:quant-ph/9909073
- categories:
- quant-ph
- comments:
- 3 pages, revtex. New title, and presentation substantially revised,
focus now being on the characterization of probability measures on the set of
effects rather than the question of hidden variables
- doi:
- 10.1103/PhysRevLett.91.120403
- arxiv_id:
- quant-ph/9909073
- journal_ref:
- Phys. Rev. Lett. 91, 120403 (2003)
- created:
- 1999-09-23
- updated:
- 2003-05-28
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