Skip to main content
Log in

Quantum Computational Structures: Categorical Equivalence for Square Root qMV -algebras

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

In this paper we investigate a categorical equivalence between square root qMV -algebras (a variety of algebras arising from quantum computation) and a category of preordered semigroups.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aharanov, D., A. Kitaev, and N. Nisan, ‘Quantum circuits with mixed states’, Proc. 13th Annual ACM Symp. on Theory of Computation 20–30, 1997.

  2. Cattaneo G., Dalla Chiara M.L., Giuntini R., Leporini R.: ‘An unsharp logic from quantum computation’. Int. J. Theor. Phys. 43, 1803–1817 (2004)

    Article  Google Scholar 

  3. Cignoli R., D’Ottaviano I., Mundici D.: Algebraic foundations of manyvalued reasoning. Kluwer, Dordrecht-Boston-London (2000)

    Google Scholar 

  4. Dalla Chiara M.L., Giuntini R., Greechie R.: Reasoning in Quantum Theory. Kluwer, Dordrecht (2004)

    Google Scholar 

  5. Domenech G., Freytes H.: ‘Fuzzy propositional logic associated with quantum computational gates’. Int. J. Theor. Phys. 34, 228–261 (2006)

    Article  Google Scholar 

  6. Dunn J.M., Hagge T.J., Moss L.S., Wang Z.: ‘Quantum logic as motived by quantum computing’. J. Symbolic Logic 70, 353–359 (2005)

    Article  Google Scholar 

  7. Freytes H., Ledda A.: ‘Categories of semigroups in quantum computational structures’. Math. Slovaca 59, 413–432 (2009)

    Article  Google Scholar 

  8. Freytes, H., A. Ledda, and G. Sergioli, ‘Stone-Weierstrass type theorem in the framework of irreversible quantum computation’, submitted to the Int. J. Theor. Phys., 2008.

  9. Giuntini R., Ledda A., Paoli F.: ‘Expanding quasi-MV algebras by a quantum operator’. Studia Logica 87, 99–128 (2007)

    Article  Google Scholar 

  10. Gudder S.: ‘Quantum computational logic’. Int. J. Theor. Phys. 42, 39–47 (2003)

    Article  Google Scholar 

  11. Gudder S., Greechie R.: ‘Sequential products on effect algebras’. Rep. Math. Phys. 49, 87–111 (2002)

    Article  Google Scholar 

  12. Gudder S., Greechie R.: ‘Uniqueness and order in sequential effect algebras’. Int. J. Theor. Phys. 44, 755–770 (2005)

    Article  Google Scholar 

  13. Kraus, K., States, effects and operations, Springer-Verlag, 1983.

  14. Ledda A., Konig M., Paoli F., Giuntini R.: ‘MV algebras and quantum computation’. Studia Logica 82, 245–270 (2006)

    Article  Google Scholar 

  15. Paoli F., Ledda A., Giuntini R., Freytes H.: ‘On some properties of QMV algebras and \({\sqrt\prime}\) QMV algebras’. Rep. Math. Logic 44, 53–85 (2008)

    Google Scholar 

  16. Tarasov V.: ‘Quantum computer with Mixed States and Four-Valued Logic’. J. Phys. A 35, 5207–5235 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hector Freytes.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Freytes, H. Quantum Computational Structures: Categorical Equivalence for Square Root qMV -algebras. Stud Logica 95, 63–80 (2010). https://doi.org/10.1007/s11225-010-9250-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-010-9250-x

Keywords

Navigation