2018/06/19 by Arkady Bolotin, Bolotin, Arkady
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #FOS: Physical sciences #Logic (math.LO) #Logic, Reasoning, and Knowledge #Quantum Physics (quant-ph) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1806.08227
openalex publication_date 2018/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As it is known, the set of all closed linear subspaces of a Hilbert space\ntogether with a binary relation over the set represents the logic of the\nquantum propositions. It is also known that the lattices of the closed linear\nsubspaces on a Hilbert space of dimension 3 or greater do not have a prime\nfilter, hence those lattices do not allow a valuation map. In contrast to that,\nfor qubits it is easy to find prime filters in the Hilbert lattice. This begs\nthe question: What assumption(s) related to the lattices of the closed linear\nsubspaces should be added or altered to preclude the bivaluation map in the\ntwo-dimensional case? The presented paper offers the answer to this question.\n