Quantum kolmogrov complexity and its applications

International Journal of Quantum Information

Volumn 5, Issue 5, 2007, Pages 729-750

  Mora, Caterina E ^a   Briegel, Hans J ^a,b   Kraus, Barbara ^b  

^a ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^b UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

Communication complexity; Entanglement; Information theory; Quantum Kolmogorov complexity

Indexed keywords

COMPUTATIONAL COMPLEXITY; INFORMATION THEORY; QUANTUM COMPUTERS; THERMODYNAMICS;

BINARY STRING; CLASSICAL BITS; CLASSICAL COMMUNICATION; COMMUNICATION COMPLEXITY; ENTANGLEMENT; ITS APPLICATIONS; KOLMOGOROV COMPLEXITY; N-QUBIT STATE;

QUANTUM ENTANGLEMENT;

EID: 35948994163     PISSN: 02197499     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219749907003171     Document Type: Article

References (31)

1. C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27 (1948) 379.
2. A. N. Kolmogorov, Three approaches to the quantitative definition of information, Probl. Inform. Transmission 1 (1965) 1.
3. G. J. Chaitin, On the length of programs for computing finite binary sequences, J. ACM 13 (1966) 547.
4. M. Li and P. Vitanyi, An Introduction to Kolmogorov Complexity and Its Applications (Springer, 1997).
5. T. M. Cover and J. A. Thomas, Elements of Information Theory (John Wiley and Sons, 1991).
6. C. H. Bennett, Complexity in the universe, in Physical Origins of Time Asymmetry, eds. J. J. Halliwell, J. Perez-Mercader and W. H. Zurek (Cambridge University Press, 1994).
7. K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I, Monatshefte für Mathematik and Physik 38 (1931) 173.
8. C. H. Bennett, The thermodynamics of computation - A review, Int. J. Theoret. Phys. 21 (1982) 305.
9. W. H. Zurek, Thermodynamic cost of computation, algorithmic complexity and the information metric, Nature 341 (1989) 119.
10. C. M. Caves, Information and entropy, Phys. Rev. E 47 (1993) 6.
11. C. M. Caves, Information, entropy and chaos, in Physical Origins of Time Asymmetry, eds. J. J. Halliwell, J. Perez-Mercader and W. H. Zurek (Cambridge University Press, 1994).
12. P. Gàcs, Quantum algorithmic entropy, arXiv: Quant-ph/0011046 v2 (2001).
13. A. Berthiaume, W. van Dam and S. Laplante, Quantum Kolmogorov complexity, arXiv: Quant-ph/005018 (2000).
14. P. Vitanyi, Three Approaches to the quantitative definition of information in an individual pure quantum state, arXiv: Quant-ph/9907035 (2000).
15. C. Mora and H. Briegel, Algorithmic complexity and entanglement of quantum states, Phys. Rev. Lett. 95 (2005) 20.
16. H. Buhrman, R. Cleve, J. Watrous and R. de Wolf, Quantum fingerprinting, Phys. Rev. Lett. 87 (2001) 16.
17. C. Mora and H. Briegel, Algorithmic complexity of quantum states, quant-ph/0412172, to appear in IJQI.
18. L. A. Levin, On the notion of a random sequence, Sov. Math. Doklady 14 (1973) 1413.
19. W. H. Zurek, Algorithmic randomness and physical entropy, Phys. Rev. A 40 (1989) 4731.
20. C. M. Caves and R. Schack, Unpredictability, information, and chaos, Complexity 3 (1997) 46-57.
21. J. Eisert and H. J. Briegel, Phys. Rev. A 64 (2001) 022306.
22. A. C.-C. Yao, Some complexity questions related to distributive computing, in Proceedings of the 11th Annual ACM Symposium on Theory of Computing (ACM, New York, 1979), p. 209.
23. R. de Wolf, Quantum computing and communication complexity, PhD thesis, University of Amsterdam (2001).
24. A. Ambainis, Algorithmica 16 (1996) 298.
25. I. Newman and M. Szegedy, Public versus private coin flips in one round communication games, in Proceedings of the 28th Annual ACM Symposium on Theory of Computing (ACM, New York, 1996), p. 596.
26. J. Justesen, A class of constructive asymptotically good algebraic codes, IEEE Trans. Inform. Theory 18 (1972) 652.
27. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. (Cambridge University Press, 2000).
28. Y. Shi, Tensor norms and the classical communication complexity of nonlocal quantum measurement, in Proceedings of the 37th A CM Symposium on Theory of Computing. (ACM, New York, 2005), p. 460.
29. R. Jozsa and N. Linden, Soc. Lond. A 459 (2003) 2011.
30. H. S. Leff and A. F. Rex (eds.), Maxwell's demon, 2: Entropy, classical and quantum information (IOP Publishing, 2003).
31. R. Landauer, Irreversibility and heat generation in the computing process, IBM J. Res. Dev. 5 (1961) 183.