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Sequent Calculus Representations for Quantum Circuits [PDF]
Electronic Proceedings in Theoretical Computer Science, 2016 When considering a sequent-style proof system for quantum programs, there are certain elements of quantum mechanics that we may wish to capture, such as phase, dynamics of unitary transformations, and measurement probabilities. Traditional quantum logics
Cameron Beebe
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A Topological Study of Contextuality and Modality in Quantum Mechanics [PDF]
, 2006 Kochen-Specker theorem rules out the non-contextual assignment of values to physical magnitudes. Here we enrich the usual orthomodular structure of quantum mechanical propositions with modal operators.
B.C. Fraassen van +22 more
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Kadison’s antilattice theorem for a synaptic algebra
Demonstratio Mathematica, 2018 We prove that if A is a synaptic algebra and the orthomodular lattice P of projections in A is complete, then A is a factor if and only if A is an antilattice.We also generalize several other results of R.
Foulis David J., Pulmannová Sylvia
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PROPERTIES OF THE FORMAL CONTEXT OF ORTHOMODULAR LATTICES
Advances in Mathematics: Scientific Journal, 2022 Let $L$ be a finite Orthomodular Lattice and $T$ be the Formal Context of $L$. Then, considering $T$ as a binary symmetric matrix, we find the determinant of the formal context of the atomic amalgam $B_n+B_m$ of two Boolean algebras $\mathbf{B_{n}}$ and $
S. Shabnam, Ramananda Hs, Harsha Aj
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A Note of Filters in Effect Algebras
Chinese Journal of Mathematics, Volume 2013, Issue 1, 2013., 2013 We investigate relations of the two classes of filters in effect algebras (resp., MV‐algebras). We prove that a lattice filter in a lattice ordered effect algebra (resp., MV‐algebra) E does not need to be an effect algebra filter (resp., MV‐filter). In general, in MV‐algebras, every MV‐filter is also a lattice filter.
Biao Long Meng +3 more
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On Intuitionistic Fuzzy Context‐Free Languages
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 Taking intuitionistic fuzzy sets as the structures of truth values, we propose the notions of intuitionistic fuzzy context‐free grammars (IFCFGs, for short) and pushdown automata with final states (IFPDAs). Then we investigate algebraic characterization of intuitionistic fuzzy recognizable languages including decomposition form and representation ...
Jianhua Jin +3 more
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A priori Knowledge and the Kochen-Specker Theorem [PDF]
, 2006 We introduce and formalize a notion of "a priori knowledge" about a quantum system, and show some properties about this form of knowledge. Finally, we show that the Kochen-Specker theorem follows directly from this study. This version is a draft version,
Calude +4 more
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Advances in Mathematical Physics, Volume 2012, Issue 1, 2012., 2012 Most quantum logics do not allow for a reasonable calculus of conditional probability. However, those ones which do so provide a very general and rich mathematical structure, including classical probabilities, quantum mechanics, and Jordan algebras. This structure exhibits some similarities with Alfsen and Shultz′s noncommutative spectral theory, but ...
Gerd Niestegge, B. G. Konopelchenko
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Semilattices global valuations in the topos approach to quantum mechanics [PDF]
, 2017 In the framework of the topos approach to quantum mechanics a kind of global valuation is introduced and studied. It allows us to represent certain features related to the logical consequences of properties about quantum systems when its phase space is ...
de Ronde, Christian +2 more
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A Comparison of Implications in Orthomodular Quantum Logic—Morphological Analysis of Quantum Logic
International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012 Morphological operators are generalized to lattices as adjunction pairs (Serra, 1984; Ronse, 1990; Heijmans and Ronse, 1990; Heijmans, 1994). In particular, morphology for set lattices is applied to analyze logics through Kripke semantics (Bloch, 2002; Fujio and Bloch, 2004; Fujio, 2006).
Mitsuhiko Fujio, Shigeru Kanemitsu
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