Geodesic
Proper versus improper mixtures: Toward a~quaternionic quantum mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 157-167

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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.
Keywords: quaternionic quantum mechanics, proper mixture, improper mixture, subentity problem, semantic realism. 
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     author = {F. Masillo and G. Scolarici and S. Sozzo},
     title = {Proper versus improper mixtures: {Toward} a~quaternionic quantum mechanics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a14/}
}
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F. Masillo; G. Scolarici; S. Sozzo. Proper versus improper mixtures: Toward a~quaternionic quantum mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 157-167. http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a14/