Experimental evidence of quantum randomness incomputability

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 82, Issue 2, 2010, Pages

  Calude, Cristian S ^a   Dinneen, Michael J ^a   Dumitrescu, Monica ^b   Svozil, Karl ^c  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b UNIVERSITY OF BUCHAREST   (Romania)

^c VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMIC INFORMATION THEORY; ASYMPTOTIC PROPERTIES; EXPERIMENTAL EVIDENCE; PSEUDORANDOMNESS; QUANTUM RANDOMNESS; TESTS OF RANDOMNESS;

INFORMATION THEORY;

RANDOM PROCESSES;

EID: 77955827767     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.82.022102     Document Type: Article

References (44)

1. M. Born, Z. Phys. EPJAFV 1434-6001 10.1007/BF01397477 37, 863 (1926).
2. M. Born, Z. Phys. EPJAFV 1434-6001 10.1007/BF01397184 38, 803 (1926).
3. A. Zeilinger, Nature (London) NATUAS 0028-0836 10.1038/438743a 438, 743 (2005).
4. C. S. Calude and K. Svozil, Adv. Sci. Lett. 1, 165 (2008).
5. P. Martin-Löf, Inform. Control IFCNA4 0019-9958 10.1016/S0019- 9958(66)80018-9 9, 602 (1966).
6. G. J. Chaitin, Exploring Randomness (Springer Verlag, London, 2001).
7. C. Calude, Information and Randomness-An Algorithmic Perspective, 2nd ed. (Springer, Berlin, 2002).
8. K. Svozil, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(90)90408-G 143, 433 (1990).
9. J. G. Rarity, M. P. C. Owens, and P. R. Tapster, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500349414552281 41, 2435 (1994).
10. T. Jennewein, U. Achleitner, G. Weihs, H. Weinfurter, and A. Zeilinger, Rev. Sci. Instrum. RSINAK 0034-6748 10.1063/1.1150518 71, 1675 (2000).
11. A. Stefanov, N. Gisin, O. Guinnard, L. Guinnard, and H. Zbinden, J. Mod. Opt. 47, 595 (2000).
12. M. Hai-Qiang, W. Su-Mei, Z. Da, C. Jun-Tao, J. Ling-Ling, H. Yan-Xue, and W. Ling-An, Chin. Phys. Lett. CPLEEU 0256-307X 10.1088/0256-307X/21/10/027 21, 1961 (2004).
13. P. X. Wang, G. L. Long, and Y. S. Li, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.2338830 100, 056107 (2006).
14. M. Fiorentino, C. Santori, S. M. Spillane, R. G. Beausoleil, and W. J. Munro, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.032334 75, 032334 (2007).
15. K. Svozil, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.054306 79, 054306 (2009).
16. G. Marsaglia [http://www.stat.fsu.edu/pub/diehard/].
17. A. Rukhin, nist Special Publ. 800-22 (National Institute of Standards and Technology, Washington DC, 2001) [http://csrc.nist.gov/groups/ST/toolkit/rng/ documents/SP800-22b.pdf].
18. P. L'Ecuyer and R. Simard, ACM Trans. Math. Software (TOMS) ACMSCU 0098-3500 10.1145/1268776.1268777 33, 22 (2007).
19. ID Quantique SA, quantis (idQuantique, Geneva, Switzerland, 2001-2010) [http://www.idquantique.com/images/stories/PDF/quantis-random-generator/ quantis-whitepaper.pdf].
20. T. Jennewein, Institut für Quantenoptik und Quanteninformation, Quantum random number generator (private communication).
21. Wolfram Research, Inc., mathematica Version 6.0 (Wolfram Research, Waterloo, Ontario, 2007) [http://reference.wolfram.com/mathematica/tutorial/ RandomNumberGeneration.html].
22. Maplesoft, maple Version 11 (Maplesoft, Champaign, IL, 2007) [http://www.maplesoft.com/support/help/Maple/view.aspx?path=rand].
23. Y. Kanada and D. Takahashi, Calculation of π up to 4 294 960 000 decimal digits, University of Tokyo (1995), [ftp://pi.super-computing.org].
24. J. von Neumann, National Bureau of Standards Applied Math Series 12, 36 (1951)
25. reprinted in John von Neumann, Collected Works, Vol. V, edited by, A. H. Traub, (MacMillan, New York, 1963), pp. 768-770.
26. I. Borel, Rendiconti del Circolo Matematico di Palermo RCMMAR 0009-725X 10.1007/BF03019651 27, 247 (1909).
27. P. Hertling, J. Universal Comput. Sci. 8, 235 (2002).
28. C. S. Calude, M. J. Dinneen, M. Dumitrescu, and K. Svozil, Report CDMTCS-372 (Centre for Discrete Mathematics and Theoretical Computer Science, University of Auckland, Auckland, New Zealand, 2009)
29. e-print arXiv: 0912.4379.
30. B. Y. Ryabko and A. I. Pestunov, Prob. Peredachi Inf. 40, 73 (2004).
31. B. Y. Ryabko and V. A. Monarev, J. Statist. Plan. Inference RCMMAR 0378-3758 10.1016/j.jspi.2004.02.010 133, 95 (2005).
32. R. Solovay and V. Strassen, SIAM J. Comput. SMJCAT 0097-5397 10.1137/0206006 6, 84 (1977). Corrigendum in [42].
33. G. J. Chaitin and J. T. Schwartz, Commun. Pure Appl. Math. SMJCAT 0010-3640 10.1002/cpa.3160310407 31, 521 (1978).
34. R. G. Pinch, e-print arXiv: math.NT/9803082.
35. R. G. Pinch, in Proceedings of Conference on Algorithmic Number Theory 2007. TUCS General Publication No. 46, edited by, A.-M. Ernvall-Hytönen,,, M. Jutila,,, J. Karhumäki,, and, A. Lepistö, (Turku Centre for Computer Science, Turku, Finland, 2007), pp. 129-131.
36. C. Calude and M. Zimand, Int. J. Comput. Math. IJCMAT 0020-7160 10.1080/00207168408803423 16, 47 (1984).
37. J. Ziv and A. Lempel, IEEE Trans. Inf. Theory IETTAW 0018-9448 10.1109/TIT.1978.1055934 24, 530 (1978).
38. C. Calude, in Developments in Language Theory, edited by, G. Rozenberg, and, A. Salomaa, (World Scientific, Singapore, 1994), pp. 113-129.
39. A. D. Wyner, IEEE Information Theory Society (1994).
40. W. J. Conover, Practical Nonparametric Statistics (Wiley, New York, 1999), p. 584.
41. S. S. Shapiro and M. B. Wilk, Biometrika BIOKAX 0006-3444 10.1093/biomet/52.3-4.591 52, 591 (2005).
42. B. L. Welch, Biometrika BIOKAX 0006-3444 10.2307/2332510 34, 28 (1947).
43. M. Davis, Computability and Unsolvability (McGraw-Hill, New York, 1958).
44. R. Solovay and V. Strassen, SIAM J. Comput. SMJCAT 0097-5397 10.1137/0207009 7, 118 (1978).