A Gleason-type theorem for qubits based on mixtures of projective measurements

Stefan Ludwig Otto Weigert, Victoria J Wright

Research output: Contribution to journalArticlepeer-review


We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of projective measurements and their classical mixtures. This assumption is significantly weaker than those required for existing Gleason-type theorems valid in dimension two.
Original languageEnglish
Article number055301
Number of pages19
JournalJournal of Physics A: Mathematical and Theoretical
Issue number5
Early online date18 Dec 2018
Publication statusPublished - 10 Jan 2019

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  • quant-ph
  • Gleason's theorem
  • postulates of quantum theory
  • quantum measurement
  • projective-simulable measurements
  • frame functions
  • quantum probability rule

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