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Open Quantum Systems Decoherence
Entanglement Theory Quantum Correlations
Quantum Foundations
Subalgebras of orthomodular lattices
arXiv
Authors: John Harding, Mirko Navara
Year
2010
Paper ID
11162
Status
Preprint
Abstract Read
~2 min
Abstract Words
104
Citations
N/A
Abstract
Sachs showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as well as by its poset of Boolean subalgebras BSub(L). The domain BSub(L) has recently found use in an approach to the foundations of quantum mechanics initiated by Butterfield and Isham, at least in the case where L is the orthomodular lattice of projections of a Hilbert space, or von Neumann algebra. The results here may add some additional perspective to this line of work.
Why This Paper Matters
- This paper contributes to the Quantum Foundations research area in the Quantum Articles archive.
- It adds a 2010 reference point for readers tracking recent quantum research.
- Sachs showed that a Boolean algebra is determined by its lattice of subalgebras.
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