Projection-algebras and quantum logic Article Swipe
P-algebras are a non-commutative, non-associative generalization of Boolean algebras that are for quantum logic what Boolean algebras are for classical logic. P-algebras have type where 0 is a constant, ' is unary and . is binary. Elements of X are called features. A partial order is defined on the set X of features by x <= y iff x.y = x. Features commute, i.e., x.y = y.x iff x.y <= x. Features x and y are said to be orthogonal iff x.y = 0 and orthogonality is a symmetric relation.The operation + is defined as the dual of . and it is commutative on orthogonal features. The closed subspaces of a separable Hilbert space form a P-algebra under orthogonal complementation and projection of a subspace onto another one.P-algebras are complemented orthomodular posets but they are not lattices. Existence of least upper bounds for ascending sequences is equivalent to the existence of least upper bounds for countable sets of pairwise orthogonal elements. Atomic algebras are defined and their main properties are studied. The logic of P-algebras is then completely characterized. The language contains a unary connective corresponding to the operation ' and a binary connective corresponding to the operation ".". It is a substructural logic of sequents where the Exchange rule is extremely limited. It is proved to be sound and complete for P-algebras.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2402.07042
- https://arxiv.org/pdf/2402.07042
- OA Status
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- Related Works
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- OpenAlex ID
- https://openalex.org/W4391800724
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https://openalex.org/W4391800724Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2402.07042Digital Object Identifier
- Title
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Projection-algebras and quantum logicWork title
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preprintOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-02-10Full publication date if available
- Authors
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Daniel LehmannList of authors in order
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https://arxiv.org/abs/2402.07042Publisher landing page
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https://arxiv.org/pdf/2402.07042Direct link to full text PDF
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2402.07042Direct OA link when available
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Quantum logic, Projection (relational algebra), Quantum, Computer science, Algebra over a field, Physics, Mathematics, Pure mathematics, Quantum mechanics, Algorithm, Quantum computerTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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