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2008 | 18 | 3 | 341-359
Tytuł artykułu

Natural quantum operational semantics with predicates

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A general definition of a quantum predicate and quantum labelled transition systems for finite quantum computation systems is presented. The notion of a quantum predicate as a positive operator-valued measure is developed. The main results of this paper are a theorem about the existence of generalised predicates for quantum programs defined as completely positive maps and a theorem about the existence of a GSOS format for quantum labelled transition systems. The first theorem is a slight generalisation of D'Hondt and Panagaden's theorem about the quantum weakest precondition in terms of discrete support positive operator-valued measures.
Rocznik
Tom
18
Numer
3
Strony
341-359
Opis fizyczny
Daty
wydano
2008
otrzymano
2007-04-17
poprawiono
2007-08-18
poprawiono
2008-05-05
Twórcy
  • Institute of Control and Computation Engineering, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland
  • Institute of Control and Computation Engineering, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland
Bibliografia
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  • Bennett C.H., Brassard G., Crepeau C., Jozsa R., Peres A. and Wooters W.K. (1993). Teleporting an unknown state via dual classical and Einstein-Podolsky-Rosen channels, Physical Review Letters 70(13): 1895-1899.
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  • Bloom B., Istrail S., Meyer A.R. (1989). Bisimulation can't be traced: Preliminary report, Conference Record of the 15th Annual ACM Symposium on Principles of Programming Languages, San Diego, CA, USA, pp. 229-239.
  • Boschi D., Branca S., de Martini F., Hardy L. and Popescu S. (1998). Experimental realization of teleporting an unknown pure quantum state via dual classical and EinsteinPodolsky-Rosen channels, Physical Review Letters 80(6): 1121-1125.
  • Bouwmeester D., Pan J.W., Mattle K., Eibl M., Weinfurter H. and Zeilinger A. (1997). Experimental quantum teleportation, Nature 390(6660): 575-579.
  • Choi M.D. (1975). Completely positive linear maps on complex matrices, Linear Algebra and Its Applications 10(3): 285-290.
  • Coecke B. and Martin K. (2002). A partial order on classical and quantum states, Technical report, PRG-RR-02-07, Oxford University.
  • Deutsch D. and Jozsa R. (1992). Rapid solutions of problems by quantum computation, Proceedings of the Royal Society of London A, 439(1907): 553-558.
  • Dijkstra E. W. (1976). A Discipline of Programming, PrenticeHall, Englewood Cliffs, NJ.
  • D'Hondt E. and Panangaden P. (2006). Quantum weakest preconditions, Mathematical Structures in Computer Science 16(3): 429-451.
  • Gielerak R. and Sawerwain M. (2007). Generalised quantum weakest preconditions, available at: arXiv:quant-ph/0710.5239v1.
  • Gleason A. M. (1957). Measures on the closed subspaces of a Hilbert space, Journal of Mathematics and Mechanics 6(4): 885-893.
  • Grover L. K. (1996). A fast quantum-mechanical algorithm for database search, Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, Philadelphia, PA, USA, ACM Press, New York, NY, pp. 212-219.
  • Hirvensalo M. (2001). Quantum Computing, Springer-Verlag, Berlin.
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  • Jozsa R. (2005). An introduction to measurement based quantum computation, available at: arXiv:quant-ph/0508124.
  • Kraus K. (1983). State, Effects, and Operations, Springer, Berlin.
  • Kak S. (2003). Teleportation protocols requiring only one classical bit, available at: arXiv:quant-ph/0305085v4.
  • Lalire M., Jorrand P. (2004). A process algebraic approach to concurrent and distributed quantum computation: Operational semantics, Proceedings of the 2nd International Workshop on Quantum Programming Languages, Turku, Finland, pp. 109-126.
  • Löwner K. (1934): Über monotone Matrixfunktionen, Mathematische Zeitschrift 38(1): 177-216.
  • Mlnařík H. (2006): LanQ-Operational Semantics of Quantum Programming Language LanQ, Technical report FIMURS-2006-10, available at: http://www.muni.cz/research/publications/706560.
  • Mauerer W. (2005). Semantics and simulation of communication in quantum programming, M.Sc. thesis, University Erlangen-Nuremberg Erlangen, Nürnberg, see: arXiv:quant-ph/0511145.
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  • Peres A. (1995). Quantum Theory: Concepts and Methods, Kluwer Academic Publishers, Dordrecht.
  • Plotkin G.D. (2004). A structural approach to operational semantics, Journal of Logic and Algebraic Programming 60: 17-139.
  • Raynal P. (2006). Unambiguous state discrimination of two density matrices in quantum information theory, Ph.D. thesis, Institut für Optik, Information und Photonik, Max Planck Forschungsgruppe, see: arXiv:quant-ph/0611133.
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  • Raussendorf R., Briegel H.J. (2001). A one-way quantum computer, Physical Review Letters 86(22): 5188-5191, see: arXiv:quant-ph/0010033.
  • Raussendorf R., Browne D.E., Briegel H.J. (2003). Measurement-based quantum computation with cluster states, Physical Review A, 68(2), 022312, see: arXiv:quant-ph/0301052.
  • Sawerwain M., Gielerak R. and Pilecki J. (2006). Operational semantics for quantum computation, in: Węgrzyn S., Znamirowski L., Czachórski T., Kozielski S. (Eds.), New Technologies in Computer Networks, WKiŁ, Warsaw, Vol. 1, pp. 69-77, (in Polish).
  • Selinger P.: (2004): Towards a quantum programming language, Mathematical Structures in Computer Science 14(5): 527-586.
  • Selinger P.: (2004). Towards a semantics for higher order quantum computation, Proceedings of the 2nd International Workshop on Quantum Programming Languages, Turku, Finland, pp. 127-143.
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Bibliografia
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