A qualitative approach to quantum probability

Ehud Lehrer, Eran Shmaya*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Pages (from-to)2331-2344
Number of pages14
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2072
StatePublished - 2006


  • Decision theory
  • Qualitative probability subjective probability
  • Quantum probability


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