Proper versus improper mixtures: Toward a quaternionic quantum mechanics

Fabio Masillo, Sandro Sozzo

Research output: Contribution to journalArticlepeer-review


The density operators obtained by taking partial traces represent improper mixtures of subsystems of a compound physical system because the coefficients in the convex sums expressing them never bear the ignorance interpretation. Assigning states to these subsystems is consequently problematic in standard quantum mechanics (subentity problem). In the semantic realism interpretation of quantum mechanics, it is instead proposed to consider improper mixtures true nonpure states conceptually distinct from proper mixtures. Based on this proposal, we show that proper and improper mixtures can be represented by different density operators in the quaternionic formulation of quantum mechanics and can hence be distinguished even from a mathematical standpoint. We provide a simple example related to the quantum theory of measurement.
Original languageEnglish
Pages (from-to)1007-1014
Number of pages8
JournalTheoretical and Mathematical Physics (TMP)
Publication statusPublished - 2009


  • Quaternionic quantum mechanics
  • Proper and improper mixtures
  • Subentity problem
  • Semantic realism


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