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| related topics |
| {observables, space, algebra} |
| {time, decoherence, evolution} |
| {let, theorem, proof} |
| {bell, inequality, local} |
| {particle, mechanics, theory} |
| {qubit, qubits, gate} |
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| {state, phys, rev} |
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Orthocomplementation and compound systems
Boris Ischi
abstract: 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0410085
- categories:
- quant-ph
- comments:
- Submitted for the proceedings of the 2004 IQSA's conference in
Denver. Revised version
- doi:
- 10.1007/s10773-005-8016-0
- arxiv_id:
- quant-ph/0410085
- created:
- 2004-10-12
- updated:
- 2005-03-18
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