Certifiable quantum dice

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 370, Issue 1971, 2012, Pages 3432-3448

  Vazirani, Umesh ^a   Vidick, Thomas ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Certifiable; Entanglement; Extractors; Randomness; Turing

Indexed keywords

STATISTICAL TESTS;

CERTIFIABLE; ENTANGLEMENT; EXTRACTORS; RANDOMNESS; TURING;

QUANTUM THEORY;

EID: 84862849462     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2011.0336     Document Type: Article

References (28)

1. Campbell-Kelly, M. 1980 Programming the mark. I. Early programming activity at the university of Manchester. Ann. Hist. Comput. 2, 136. (doi:10.1109/MAHC.1980.10018)
2. Taylor, G. & Cox, G. 2011 Behind intel's new random-number generator. IEEE Spectr. September, 32-35.
3. Downey, R. & Hirschfeldt, D. 2010 Algorithmic randomness and complexity. Berlin, Germany: Springer.
4. Goldreich, O. 2010 Pseudorandom generators: a primer. See http://www.wisdom.weizmann. ac.il/õded/prg-primer.html.
5. Santha, M. & Vazirani, U. V. 1984 Generating quasi-random sequences from slightly-random sources. In Proc. of the 25th Annu. Symp. on Foundations of Computer Science, Singer Island, FL, 24-26 October 1984, pp. 434-440. Washington, DC: IEEE Computer Society. (Pubitemid 16526277)
6. Zuckerman, D. 1990 General weak random sources. In Proc. 31st Annu. Symp. on Foundations of Computer Science, St. Louis, MO, 22-24 October 1990, pp. 534-543. Washington, DC: IEEE Computer Society. (Pubitemid 21663248)
7. Shaltiel, R. 2002 Recent developments in explicit constructions of extractors. Bull. Eur. Assoc. Theor. Comput. Sci. 77, 67-95.
8. Stefanov, A., Gisin, N., Guinnard, O., Guinnard, L. & Zbinden, H. 2000 Optical quantum random number generator. J. Mod. Opt. 47, 595-598. (http://arxiv.org/abs/qrant-ph/9907006) (Pubitemid 35392946)
9. Wang, P. X., Long, G. L. & Li, Y. S. 2006 Scheme for a quantum random number generator. J. Appl. Phys. 100, 056 107. (doi:10.1063/1.2338830) (Pubitemid 44422119)
10. Svozil, K. 1990 The quantum coin toss-testing microphysical undecidability. Phys. Lett. A 143, 433-437. (doi:10.1016/0375-9601 (90) 90408-G)
11. Fiorentino, M., Santori, C., Spillane, S. M., Beausoleil, R. G. & Munro, W. J. 2007 Secure self-calibrating quantum random-bit generator. Phys. Rev. A. 75, 032 334. (doi:10.1103/PhysRevA. 75.032334)
12. Calude, C., Dinneen, M., Dumitrescu, M. & Svozil, K. 2010 Experimental evidence of quantum randomness incomputability. Phys. Rev. A. 82, 022102. (doi:10.1103/PhysRevA.82.022102)
13. Colbeck, R. 2009 Quantum and relativistic protocols for secure multi-party computation. Cambridge, UK: University of Cambridge.
14. Pironio, S. et al. 2009 Random numbers certified by Bell's theorem. Nature 464, 1021-1024. (doi:10.1038/nature09008)
15. Einstein, A., Podolsky, P. & Rosen, N. 1935 Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777-780. (doi:10.1103/PhysRev. 47.777)
16. Bell, J. S. 1964 On the Einstein-Podolsky-Rosen paradox. Physics 1, 195-200.
17. Bell, J. S. 1966 On the problem of hidden variables in quantum theory. Rev. Mod. Phys. 38, 447-452. (doi:10.1103/RevModPhys.38.447)
18. Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. 1969 Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880-884. (doi:10.1103/PhysRevLett.23.880)
19. Colbeck, R. & Kent, A. 2011 Private randomness expansion with untrusted devices. J. Phys. A Math. Theor. 44, 095 305. (doi:10.1088/1751-8113/ 44/9/095305)
20. Mayers, D. & Yao, A. 2004 Self testing quantum apparatus. Quantum Inf. Comput. 4, 273-286. (http://arxiv.org/abs/grant.ph./0307205) (Pubitemid 39080447)
21. Barrett, J., Hardy, L. & Kent, A. 2005 No signaling and quantum key distribution. Phys. Rev. Lett. 95, 010 503. (doi:10.1103/PhysRevLett.95.010503) (Pubitemid 41506418)
22. Fehr, S., Gelles, R. & Schaffner, C. 2011 Security and composability of randomness expansion from Bell inequalities. (http://arxiv.org/abs/1111.6052)
23. Bennett, C. & Brassard, G. 1984 Quantum cryptography: public key distribution and coin tossing. In Proc. of IEEE Int. Conf. on Computers, Systems, and Signal Processing, Bangalore, India, 9-12 December 1984, pp. 175-179. Washington, DC: IEEE Computer Society.
24. Pironio, S. & Massar, S. 2011 Security of practical private randomness generation. (http://arxiv.org/abs/1111.6056)
25. Terhal, B. 2004 Is entanglement monogamous? IBM J. Res. Dev. 48, 71-78. (doi:10.1147/rd.481.0071)
26. Vazirani, U. V. & Vidick, T. 2012 Certifiable quantum dice-or, true random number generation secure against quantum adversaries. (http:arxiv.org/abs/1111.6054)
27. Knuth, A. D. Y. 1976 The complexity of nonuniform random number generation. In Algorithms and complexity: new directions and recent results (ed. J. F. Traub). New York, NY: Academic Press.
28. Guruswami, V., Umans, C. & Vadhan, S. 2009 Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes. J. ACM 56, 20:1-20:34.