Natural Computing

, Volume 8, Issue 3, pp 539–546 | Cite as

On the solution of trivalent decision problems by quantum state identification

  • Karl Svozil
  • Josef Tkadlec


The trivalent functions of a trit can be grouped into equipartitions of three elements. We discuss the separation of the corresponding functional classes by quantum state identifications.


Trivalent decision problems Quantum computation Quantum decision problems Quantum state identification Entanglement Generalized Deutsch problem 



The work was supported by the research plan of the Ministry of Education of the Czech Republic No. 6840770010 and by the grant of the Grant Agency of the Czech Republic No. 201/07/1051 and by the exchange agreement of both of our universities.


  1. Beals R, Buhrman H, Cleve R, Mosca M, de Wolf R (2001) Quantum lower bounds by polynomials. J ACM 48:778–797. Google Scholar
  2. Bennett CH, Bernstein E, Brassard G, Vazirani U (1997) Strengths and weaknesses of quantum computing. SIAM J Comput 26:1510–1523. Google Scholar
  3. Brukner Č, Zeilinger A (1999a) Malus’ law and quantum information. Acta Physica Slovaca 49:647–652Google Scholar
  4. Brukner Č, Zeilinger A (1999b) Operationally invariant information in quantum mechanics. Phys Rev Lett 83:3354–3357MATHCrossRefMathSciNetGoogle Scholar
  5. Brukner Č, Zeilinger A (2003) Information and fundamental elements of the structure of quantum theory. In: Castell L, Ischebek O (eds) Time, quantum and information, Springer, Berlin, pp 323–355Google Scholar
  6. Brukner Č, Zukowski M, Zeilinger A (2002) The essence of entanglement. Translated to Chinese by Qiang Zhang and Yond-de Zhang, New advances in physics (J Chin Phys Soc).
  7. Cleve R (2000) An introduction to quantum complexity theory. In: Macchiavello C, Palma G, Zeilinger A (eds) Collected papers on quantum computation and quantum information theory. World Scientific, Singapore, pp 103–127Google Scholar
  8. Cleve R, Ekert A, Macchiavello C, Mosca M (1998) Rapid solution of problems by quantum computation. Proc R Soc A Math Phys Eng Sci 454:339–354.
  9. Deutsch D (1985) Quantum theory, the Church-Turing principle and the universal quantum computer. Proc R Soc Lond Ser A Math Phys (1934–1990) 400:97–117.
  10. Deutsch D, Jozsa R (1992) Rapid solution of problems by quantum computation. Proc R Soc Math Phys Sci (1990–1995) 439:553–558.
  11. Donath N, Svozil K (2002) Finding a state among a complete set of orthogonal ones. Phys Rev A (Atomic, Molecular, and Optical Physics) 65:044 302.
  12. Farhi E, Goldstone J, Gutmann S, Sipser M (1998) Limit on the speed of quantum computation in determining parity. Phys Rev Lett 81:5442–5444. Google Scholar
  13. Fortnow L (2003) One complexity theorist’s view of quantum computing. Theor Comput Sci 292:597–610.
  14. Gruska J (1999) Quantum computing. McGraw-Hill, LondonGoogle Scholar
  15. Mermin ND (2003) From Cbits to Qbits: teaching computer scientists quantum mechanics. Am J Phys 71:23–30. Google Scholar
  16. Mermin ND (2007) Quantum computer science. Cambridge University Press, CambridgeMATHGoogle Scholar
  17. Miao X (2001) A polynomial-time solution to the parity problem on an NMR quantum computer. eprint: arXiv: quant-ph/0108116Google Scholar
  18. Nielsen MA, Chuang IL (2000) Quantum computation and quantum information. Cambridge University Press, CambridgeMATHGoogle Scholar
  19. Odifreddi P (1989) Classical recursion theory, vol 1. North-Holland, AmsterdamGoogle Scholar
  20. Orus R, Latorre JI, Martin-Delgado MA (2004) Systematic analysis of majorization in quantum algorithms. Eur Phys J D 29:119–132. Google Scholar
  21. Ozhigov Y (1998) Quantum computer can not speed up iterated applications of a black box. Lect Notes Comput Sci 1509:152–159.
  22. Rogers H Jr (1967) Theory of recursive functions and effective computability. McGraw-Hill, New YorkMATHGoogle Scholar
  23. Stadelhofer R, Suterand D, Banzhaf W (2005) Quantum and classical parallelism in parity algorithms for ensemble quantum computers. Phys Rev A (Atomic, Molecular, and Optical Physics) 71:032345. Google Scholar
  24. Svozil K (2006) Characterization of quantum computable decision problems by state discrimination. In: Adenier G, Khrennikov A, Nieuwenhuizen TM (eds) Quantum theory: reconsideration of foundations–3, vol 810, pp 271–279.
  25. Svozil K (2002) Quantum information in base n defined by state partitions. Phys Rev A (Atomic, Molecular, and Optical Physics) 66:044306.
  26. Svozil K (2004) Quantum information via state partitions and the context translation principle. J Mod Opt 51:811–819. Google Scholar
  27. Zeilinger A (1999) A foundational principle for quantum mechanics. Found Phys 29:631–643. Google Scholar

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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikVienna University of TechnologyViennaAustria
  2. 2.Department of Mathematics, Faculty of Electrical EngineeringCzech Technical UniversityPrahaCzech Republic

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