The usual formulation of quantum theory is based onrather obscure axioms (employing complex Hilbertspaces, Hermitean operators, and the trace formulafor calculating probabilities). In this paper it isshown that quantum theory can be derived from vevery reasonable axioms. The rst four of these axiomsare obviously consistent with both quantum theoryand classical probability theory. Axiom 5 (whichrequires that there exist continuous reversible transformationsbetween pure states) rules out classicalprobability theory. If Axiom 5 (or even just the word\continuous" from Axiom 5) is dropped then we obtainclassical probability theory instead. This workprovides some insight into the reasons why quantumtheory is the way it is. For example, it explains theneed for complex numbers and where the trace formulacomes from. We also gain insight into the relationshipbetween quantum theory and classical probabilitytheory.

Authors: Hardy L.  Pages: 34 Year: 2001 
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