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Keywords:
orthomodular lattice; quantum logic; symmetric difference; Boolean algebra; group-valued state
orthomodular lattice; quantum logic; symmetric difference; Boolean algebra; group-valued state
Summary:
The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of $Z_2$-valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space.
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