Nonexistence of hidden variables in the algebraic approach |
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| Authors: | Miklós Rédei |
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| Institution: | (1) Loránd Eötvös University, Rákóczi ut 5, H-1088 Budapest, Hungary |
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| Abstract: | Given two unital C*-algebrasA,  and their state spacesE
A
, E respectively, (A,E
A
) is said to have (, E) as a hidden theory via a linear, positive, unit-preserving map L:  A if, for all   E
A
, L* can be decomposed in E into states with pointwise strictly less dispersion than that of . Conditions onA and L are found that exclude (A,E
A
) from having a hidden theory via L. It is shown in particular that, ifA is simple, then no (, E) can be a hidden theory of (A,E
A
) via a Jordan homomorphism; it is proved furthermore that, ifA is a UHF algebra, it cannot be embedded into a larger C*-algebra such that (, E) is a hidden theory of (A,E
A
) via a conditional expectation from ontoA. |
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| Keywords: | |
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