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arXiv · 1806.08227

The assumption of the Hilbert lattice in the case of a two-dimensional system

Arkady Bolotin
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Abstract

As it is known, the set of all closed linear subspaces of a Hilbert space together with a binary relation over the set represents the logic of the quantum propositions. It is also known that the lattices of the closed linear subspaces on a Hilbert space of dimension 3 or greater do not have a prime filter, hence those lattices do not allow a valuation map. In contrast to that, for qubits it is easy to find prime filters in the Hilbert lattice. This begs the question: What assumption(s) related to the lattices of the closed linear subspaces should be added or altered to preclude the bivaluation map in the two-dimensional case? The presented paper offers the answer to this question.

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Arkady Bolotin. 2018-06-19. The assumption of the Hilbert lattice in the case of a two-dimensional system. https://arxiv.org/abs/1806.08227

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