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Kochen-Specker Sets and Generalized Orthoarguesian Equations (CROSBI ID 163892)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Megill, Norman D. ; Pavičić, Mladen Kochen-Specker Sets and Generalized Orthoarguesian Equations // Annales henri poincare, 12 (2011), 7; 1417-1429. doi: 10.1007/s00023-011-0109-0

Podaci o odgovornosti

Megill, Norman D. ; Pavičić, Mladen

engleski

Kochen-Specker Sets and Generalized Orthoarguesian Equations

Every set (finite or infinite) of quantum vectors (states) satisfies generalized orthoarguesian equations ($n$OA). We consider two 3-dim Kochen-Specker (KS) sets of vectors and show how each of them should be represented by means of a Hasse diagram--- a lattice, an algebra of subspaces of a Hilbert space--that contains rays and planes determined by the vectors so as to satisfy $n$OA. That also shows why they cannot be represented by a special kind of Hasse diagram called a Greechie diagram, as has been erroneously done in the literature. One of the KS sets (Peres') is an example of a lattice in which 6OA pass and 7OA fails, and that closes an open question of whether the 7oa class of lattices properly contains the 6oa class. This result is important because it provides additional evidence that our previously given proof of noa =< (n+1)oa can be extended to proper inclusion noa < (n+1)oa and that nOA form an infinite sequence of successively stronger equations.

Hilbert space; Hilbert lattice; generalized orthoarguesian equations; Kochen-Specker sets

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Podaci o izdanju

12 (7)

2011.

1417-1429

objavljeno

1424-0637

10.1007/s00023-011-0109-0

Povezanost rada

Fizika

Poveznice
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