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Reachability analysis is one of the most successful methods used in design and validation of protocols for classical communication, whereas the predicate/transition-net formalism is one of the most appropriate formalisms for reachability analysis oriented modelling. Quantum teleportation and dense coding are non-classical communication protocols that have been widely researched in the field of quantum computing. In this article, we present predicate/transition-net models of these two protocols and use the PROD reachability analysis tool for analysing the models.
Wydawca
Czasopismo
Rocznik
Tom
Strony
465--479
Opis fizyczny
bibliogr. 24 poz., tab., wykr.
Twórcy
autor
autor
- Space Systems Finland Ltd., Kappelitie 6, FI-02200 Espoo, Finland, Kimmo.varpaaniemi@kolumbus.fi
Bibliografia
- [1] Bennett, C. H., Brassard, G., Cr´epeau, C., Jozsa, R., Peres, A., Wootters, W. K.: Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels, Physical Review Letters, 70(13), 1993, 1895-1899.
- [2] Bennett, C. H., Wiesner, S. J.: Communication via One- and Two-Particle Operators on Einstein-Podolsky-Rosen States, Physical Review Letters, 69(20), 1992, 2881-2884.
- [3] Collins, D., Popescu, S.: Classical Analog of Entanglement, Physical Review A, 65(3), 2002, 032321:1-11.
- [4] D'Hondt, E.: Distributed Quantum Computation, Doctoral Dissertation, The Free University of Brussels, Belgium, 2005.
- [5] D'Hondt, E., Panangaden, P.: Reasoning About Quantum Knowledge, in: FSTTCS 2005: Foundations of Software Technology and Theoretical Computer Science (R. Ramanujam, S. Sen, Eds.), LNCS 3821, Springer-Verlag, Berlin, Germany, 2005, 553-564.
- [6] Gay, S. J., Nagarajan, R., Papanikolaou,N. K.: ProbabilisticModel-Checking of Quantum Protocols, in: Pre-Proceedings of the 2nd InternationalWorkshop on Developments in Computational Models (J.-P. Jouannaud, I. Mackie, Eds.), Venice, Italy, 2006, 63-74.
- [7] Gay, S. J., Nagarajan, R., Papanikolaou, N. K.: QMC: A Model Checker for Quantum Systems, in: Proceedings of the LQCIL'07 Workshop on Quantum Cryptography and Security (P. Mateus, A. Sernadas, Eds.), Lisbon, Portugal, 2007.
- [8] Genrich, H. J.: Predicate/Transition Nets, in: Petri Nets: Central Models and Their Properties - Advances in Petri Nets 1986, Part I (W. Brauer, W. Reisig, G. Rozenberg, Eds.), LNCS 254, Springer-Verlag, Berlin, Germany, 1987, 207-247.
- [9] Graham, A.: Kronecker Products and Matrix Calculus: with Applications, Ellis Horwood Ltd., Chichester, UK, 1981.
- [10] Hardy, L.: Spooky Action at a Distance in Quantum Mechanics, Contemporary Physics, 39(1), 1998, 419-429.
- [11] Hung, W. N. N., Song, X., Yang, G., Yang, J., Perkowski, M.: Optimal Synthesis of Multiple Output Boolean Functions Using a Set of Quantum Gates by Symbolic Reachability Analysis, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 25(9), 2006, 1652-1663.
- [12] Koniorczyk, M., Kiss, T., Janszky, J.: Teleportation: from Probability Distributions to Quantum States, Journal of Physics A: Mathematical and General, 34(35), 2001, 6949-6955.
- [13] Nering, E. D.: Linear Algebra and Matrix Theory, John Wiley & Sons, Inc., New York, NY, USA, 1970.
- [14] Nielsen, M. A., Chuang, I. L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, UK, 2000.
- [15] Ojala, L., Penttinen, O.-M., Parviainen, E.: Modeling and Analysis ofMargolus Quantum Cellular Automata Using Net-Theoretical Methods, in: Applications and Theory of Petri Nets: 25th International Conference (J. Cortadella,W. Reisig, Eds.), LNCS 3099, Springer-Verlag, Berlin, Germany, 2004, 331-350.
- [16] Papanikolaou, N. K.: Techniques for Design and Validation of Quantum Protocols,Master's Thesis, Research Report CS-RT-413, University of Warwick, Coventry, UK, 2005.
- [17] Petri Nets World (online services accessible via http://www.informatik.uni-hamburg.de/TGI/PetriNets/), University of Hamburg, Germany.
- [18] PROD 3.4.01 (reachability analysis software available via http://www.tcs.hut.fi/Software/prod/), Helsinki University of Technology, Espoo, Finland, 2006.
- [19] Stenholm, S., Suominen, K.-A.: Quantum Approach to Informatics,Wiley Interscience, Hoboken, NJ, USA, 2005.
- [20] Varpaaniemi, K., Halme, J., Hiekkanen, K., Pyssysalo, T.: PROD Reference Manual, Technical Report B13, Digital Systems Laboratory, Helsinki University of Technology, Espoo, Finland, 1995.
- [21] Varpaaniemi, K., Heljanko, K., Lilius, J.: PROD 3.2 - An Advanced Tool for Efficient Reachability Analysis, in: Computer Aided Verification: 9th International Conference (O. Grumberg, Ed.), LNCS 1254, Springer-Verlag, Berlin, Germany, 1997, 472-475.
- [22] Vernam., G. S.: Cipher Printing Telegraph Systems for SecretWire and Radio Telegraphic Communications, Journal of the American Institute of Electrical Engineers, 45, 1926, 109-115.
- [23] Wikipedia articles at the following subdirectories of http://en.wikipedia.org/wiki: Quantum entanglement, Quantum teleportation, Superdense coding, and Thread.
- [24] Zeilinger, A.: Quantum Teleportation and the Non-Locality of Information, Philosophical Transactions of the Royal Society of London, Series A, 355(1733), 1997, 2401-2404.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS5-0016-0031