Orthocomplementation and compound systems

Details Orthocomplementation and compound systems Orthocomplementation and compound systems

2004-10-12

arxiv.org/abs/quant-ph/0410085v2

Physics

Quantum Physics

Submitted for the proceedings of the 2004 IQSA's conference in Denver. Revised version

Scientific paper

10.1007/s10773-005-8016-0

In their 1936 founding paper on quantum logic, Birkhoff and von Neumann postulated that the lattice describing the experimental propositions concerning a quantum system is orthocomplemented. We prove that this postulate fails for the lattice L_sep describing a compound system consisting of so called separated quantum systems. By separated we mean two systems prepared in different ``rooms'' of the lab, and before any interaction takes place. In that case the state of the compound system is necessarily a product state. As a consequence, Dirac's superposition principle fails, and therefore L_sep cannot satisfy all Piron's axioms. In previous works, assuming that L_sep is orthocomplemented, it was argued that L_sep is not orthomodular and fails to have the covering property. Here we prove that L_sep cannot admit and orthocomplementation. Moreover, we propose a natural model for L_sep which has the covering property.

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