A Qualitative Approach to Quantum Probability
A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. The question arises as to when such an order can be represented by a quantum probability. We introduce a few behaviorally plausible axioms that provide the answer in two cases: pure state and uniform measure....
Veröffentlicht in: | Proceedings: Mathematical, Physical and Engineering Sciences. - The Royal Society. - 462(2006), 2072, Seite 2331-2344 |
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Format: | Online-Aufsatz |
Sprache: | English |
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2006
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Zugriff auf das übergeordnete Werk: | Proceedings: Mathematical, Physical and Engineering Sciences |
Schlagworte: | qualitative probability subjective probability decision theory quantum probability Mathematics Physical sciences Behavioral sciences Philosophy |
Zusammenfassung: | A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. The question arises as to when such an order can be represented by a quantum probability. We introduce a few behaviorally plausible axioms that provide the answer in two cases: pure state and uniform measure. The general problem is answered by using duality-like conditions. The general problem of characterizing the partial orders that admit a quantum representation by behaviorally justified axioms remains open. |
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ISSN: | 13645021 |