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Holistic logical arguments in quantum computation

  • Maria Luisa Dalla Chiara , Roberto Giuntini , Roberto Leporini and Giuseppe Sergioli EMAIL logo
Published/Copyright: July 1, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 2

Abstract

Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters), while logical connectives correspond to (quantum logical) gates that transform quantum information in a reversible way. The characteristic holistic features of the quantum theoretic formalism (which play an essential role in entanglement-phenomena) can be used in order to develop a holistic version of the quantum computational semantics. In contrast with the compositional character of most standard semantic approaches, meanings of formulas are here dealt with as global abstract objects that determine the contextual meanings of the formulas’ components (from the whole to the parts). We present a survey of the most significant logical arguments that are valid or that are possibly violated in the framework of this semantics. Some logical features that may appear prima facie strange seem to reflect pretty well informal arguments that are currently used in our rational activity.

MSC 2010: Primary 03C65
Key words: holistic semantics; quantum logics

Dedicated to Anatolij Dvurečenskij

(Communicated by Sylvia Pulmannová)

Sergioli’s work has been supported by the Italian Ministry of Scientific Research within the FIRB project “Structures and dynamics of knowledge and cognition”, Cagliari unit F21J12000140001 and within the RAS project: “Modeling the uncertainty: Quantum Theory and Imaging Processing”;

Leporini’s work has been supported by the Italian Ministry of Scientific Research within the PRIN project “Automata and Formal Languages: Mathematical Aspects and Applications”.

References

[1] AHARONOV, D.—KITAEV, A.—NISAN, N.: Quantum circuits with mixed states. In: STOC ’98: Proceedings of the thirtieth annual ACM symposium on Theory of computing, ACM Press, New York, 1998, pp. 20–30.10.1145/276698.276708Search in Google Scholar

[2] BELTRAMETTI, E.—DALLA CHIARA, M. L.—GIUNTINI, R.—SERGIOLI, G.: Quantum teleportation and quantum epistemic semantics, Math. Slovaca 62 (2012), 1–24.10.2478/s12175-012-0069-ySearch in Google Scholar

[3] BELTRAMETTI, E.—DALLA CHIARA, M. L.—GIUNTINI, R.—LEPORINI, R.—SERGIOLI, G.: Epistemic quantum computational structures in a Hilbert-space environment, Fund. Inform. 115 (2012), 1–14. DOI: 10.3233/FI-2012-637.10.3233/FI-2012-637Search in Google Scholar

[4] DALLA CHIARA, M. L.—GIUNTINI, R.—LEPORINI, R.: Logics from quantum computation, Internat. J. Quantum Inform. 3 (2005), 293–337.10.1142/S0219749905000943Search in Google Scholar

[5] DALLA CHIARA, M. L.—FREYTES, H.—GIUNTINI, R.—LEDDA, A.—SERGIOLI, G.: The algebraic structure of an approximately universal system of quantum computational gates, Found. Phys. 39 (2009), 559–572.10.1007/s10701-009-9302-0Search in Google Scholar

[6] DALLA CHIARA, M. L.—FREYTES, H.—GIUNTINI, R.—LEDDA, A.—LEPORINI, R.—SERGIOLI, G.: Entanglement as a semantic resource, Found. Phys. 40 (2011), 1494–1518.10.1007/s10701-010-9407-5Search in Google Scholar

[7] DALLA CHIARA, M. L.—GIUNTINI, R.—GREECHIE, R.: Reasoning in Quantum Theory, Kluwer, Dordrecht, 2004.10.1007/978-94-017-0526-4Search in Google Scholar

[8] DALLA CHIARA, M. L.—GIUNTINI, R.—NEGRI, E.—LUCIANI, A. R.: From Quantum Information to Musical Semantics, College Publications, London, 2012.Search in Google Scholar

[9] GUDDER, S.: Quantum computational logics, Internat. J. Theoret. Phys. 42 (2003), 39–47.10.1023/A:1023327005274Search in Google Scholar

[10] NIELSEN, M.—CHUANG, I.: Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.10.1017/CBO9780511976667Search in Google Scholar

Received: 2014-2-12
Accepted: 2014-8-26
Published Online: 2016-7-1
Published in Print: 2016-4-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0138
Keywords for this article
holistic semantics; quantum logics

Articles in the same Issue

  1. Research Article
  2. Holistic logical arguments in quantum computation
  3. Research Article
  4. States with values in the Łukasiewicz groupoid
  5. Research Article
  6. On realization of effect algebras
  7. Research Article
  8. States on symmetric logics: extensions
  9. Research Article
  10. Extensions and measurability in quantum measure spaces
  11. Research Article
  12. Convex subalgebras of upper bounded GMV-algebras
  13. Research Article
  14. Combining boolean algebras and ℓ-groups in the variety generated by chang’s mv-algebra
  15. Research Article
  16. Large rigid sets of algebras with respect to embeddability
  17. Research Article
  18. Conformal algebras, vertex algebras, and the logic of locality
  19. Research Article
  20. Extension of measures on pseudo-D-lattices
  21. Research Article
  22. Note on a parameter switching method for nonlinear ODEs
  23. Research Article
  24. Compatibility for probabilistic theories
  25. Research Article
  26. Completeness of Gelfand-Neumark-Segal inner product space on Jordan algebras
  27. Research Article
  28. Commutativity in a synaptic algebra
  29. Research Article
  30. Discrete averaged mixing applied to the logarithmic distributions
  31. Research Article
  32. Automorphisms of decompositions
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