Skip to main content
SpringerLink
Log in

An Unsharp Logic from Quantum Computation

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Logical gates studied in quantum computation suggest a natural logical abstraction that gives rise to a new form of unsharp quantum logic. We study the logical connectives corresponding to the following gates: the Toffoli gate, the NOT and the \(\sqrt {NOT} \) (which admit of natural physical models). This leads to a semantic characterization of a logic that we call quantum computational logic (QCL).

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  • Birkhoff, G. and von Neumann, J. (1936). The logic of quantum mechanics. Annals of Mathematics 37, 823-843.

    Google Scholar 

  • Dalla Chiara, M. L. and Giuntini, R. (2002). Quantum logics. In Handbook of Philosophical Logic, Vol. 6, G. Gabbay and F. Guenthner, eds., Kluwer, Dordrecht.

    Google Scholar 

  • Deutsch, D., Ekert, A., and Lupacchini, R. (2000). Machines, logic and quantum physics. Bulletin of Symbolic Logic 6(3), 265-283.

    Google Scholar 

  • Preskill, J. (1999). Lecture Notes in Physics. In Quantum Information and Computation, Vol. 229, Springer, Berlin.

    Google Scholar 

  • Ekert, A., Hayden, P., and Inamori, H. (2001). Basic concepts in quantum computation. In Coeherent Atomic Matter Waves Vol. LXXII of Nato Advanced Study Institute-Les Houches, R. Kaiser, C. Westbrook, and F. David, eds., Springer-Verlag, Berlin.

    Google Scholar 

  • Gudder, S. (2000). Quantum languages. In Current Research in Operational Quantum Logic, B. Coecke, D. Moore, and A. Wilce, eds., Kluwer, Dordrecht.

    Google Scholar 

  • Toffoli, T. (1980). Reversible computing. In Automata, Languages and Programming, Vol. 84, J.W. de Baker, J. van Leeuwen, eds., Springer, Berlin.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università di Milano--Bicocca, Milano, Italy

    Gianpiero Cattaneo

  2. Dipartimento di Filosofia, Università di Firenze, Firenze, Italy

    Maria Luisa Dalla Chiara

  3. Dipartimento di Scienze Pedagogiche e Filosofiche, Università di Cagliari, Cagliari, Italy

    Roberto Giuntini

  4. Dipartimento di Informatica, Sistemistica e Comunicazione, Università di Milano--Bicocca, Milano, Italy

    Roberto Leporini

Authors
  1. Gianpiero Cattaneo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maria Luisa Dalla Chiara
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roberto Giuntini
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Roberto Leporini
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cattaneo, G., Chiara, M.L.D., Giuntini, R. et al. An Unsharp Logic from Quantum Computation. International Journal of Theoretical Physics 43, 1803–1817 (2004). https://doi.org/10.1023/B:IJTP.0000048821.56239.cb

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:IJTP.0000048821.56239.cb

Search

Navigation