Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter December 20, 2012

Quantum teleportation and quantum epistemic semantics

  • Enrico Beltrametti EMAIL logo , Maria Chiara , Roberto Giuntini and Giuseppe Sergioli
From the journal Mathematica Slovaca


Quantum information gives rise to some puzzling epistemic problems that can be interestingly investigated from a logical point of view. A characteristic example is represented by teleportation phenomena, where knowledge and actions of observers (epistemic agents) play a relevant role. By abstracting from teleportation, we propose a simplified semantics for a language that consists of two parts: 1)the quantum computational sub-language, whose sentences α represent pieces of quantum information (which are supposed to be stored by some quantum systems)2)the classical epistemic sub-language, whose atomic sentences have the following forms: agent a has a probabilistic information about the sentence α; agent a knows the sentence α.

Interestingly enough, some conceptual difficulties of standard epistemic logics can be avoided in this framework.

[1] AHARONOV, A.: A simple proof that Toffoli and Hadamard are quantum universal, [arXiv:quant-ph/0301040], 2003. Search in Google Scholar

[2] AHARONOV, A.— KITAEV, A.— NISAN A.: Quantum circuits with mixed states. In: STOC’ 98: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, ACM Press, 1998, pp. 20–30. Search in Google Scholar

[3] DALLA CHIARA, M. L.— GIUNTINI, R.— FREYTES, H.— LEDDA, A.— SERGIOLI G: The algebraic structure of an approximately universal system of quantum computational gates, Found. Phys. 39 (2009), 559–572. in Google Scholar

[4] DALLA CHIARA, M. L.— GIUNTINI, R.— FREYTES, H.— LEDDA, A.— LEPORINI, R. — SERGIOLI G: Entanglement as a semantic resource, Found. Phys. 40 (2011), 1494–1518. in Google Scholar

[5] 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

[6] DALLA CHIARA, M. L.— GIUNTINI, R.— LEPORINI, R.: Logics from quantum computation, Internat. J. Quantum Inform. 3 (2005), 293–337. in Google Scholar

[7] 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. Search in Google Scholar

[8] GUDDER, S.: Quantum computational logics, Internat. J. Theoret. Phys. 42 (2003), 39–47. in Google Scholar

[9] NIELSEN, M. — CHUANG I.: Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000. Search in Google Scholar

[10] SHI, Y.: Both Toffoli and controlled-Not need little help to do universal quantum computation, [arXiv:quant-ph/0205115], 2002. Search in Google Scholar

Published Online: 2012-12-20
Published in Print: 2012-12-1

© 2012 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 5.6.2023 from
Scroll to top button