The uncertainty principle determines the nonlocality of quantum mechanics

Science

Volumn 330, Issue 6007, 2010, Pages 1072-1074

  Oppenheim, Jonathan ^a   Wehner, Stephanie ^b,c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

MEASUREMENT METHOD; QUALITATIVE ANALYSIS; QUANTUM MECHANICS; UNCERTAINTY ANALYSIS;

ARTICLE; ENTROPY; INFORMATION SCIENCE; PRIORITY JOURNAL; QUANTUM MECHANICS; QUANTUM THEORY; UNCERTAINTY;

EID: 78449266776     PISSN: 00368075     EISSN: 10959203     Source Type: Journal    
DOI: 10.1126/science.1192065     Document Type: Article

References (24)

1. W. Heisenberg, Z. Phys. 43, 172 (1927).
2. J. S. Bell, Physics 1, 195 (1965).
3. S. Popescu, D. Rohrlich, Found. Phys. 24, 379 (1994).
4. G. V. Steeg, S. Wehner, QIC 9, 801 (2009).
5. M. Pawłowski et al., Nature 461, 1101 (2009).
6. W. van Dam, http://arxiv.org/abs/quant-ph/0501159 (2005).
7. H. Barnum, S. Beigi, S. Boixo, M. B. Elliott, S. Wehner, Phys. Rev. Lett. 104, 140401 (2010).
8. D. Deutsch, Phys. Rev. Lett. 50, 631 (1983).
9. I. Białynicki-Birula, J. Mycielski, Commun. Math. Phys. 44, 129 (1975).
10. S. Wehner, A. Winter, N. J. Phys. 12, 025009 (2010).
11. Without loss of generality, we assume that each measurement has the same set of possible outcomes, because we may simply add additional outcomes that never occur.
12. See supporting material on Science Online.
13. S. Wehner, M. Christandl, A. C. Doherty, Phys. Rev. A 78, 062112 (2008).
14. J. Clauser, M. Horne, A. Shimony, R. Holt, Phys. Rev. Lett. 23, 880 (1969).
15. B. Cirel'son (Tsirelson), Lett. Math. Phys. 4, 93 (1980).
16. E. Schrödinger, M. Born, Proc. Camb. Philos. Soc. 31, 555 (1935).
17. E. Schrödinger, P. A. M. Dirac, Proc. Camb. Philos. Soc. 32, 446 (1936).
18. H. M. Wiseman, S. J. Jones, A. C. Doherty, Phys. Rev. Lett. 98, 140402 (2007).
19. S. J. Jones, H. M. Wiseman, A. C. Doherty, Phys. Rev. A 76, 052116 (2007).
20. H. Barnum, C. Gaebler, A. Wilce, http://arxiv.org/abs/ 0912.5532 (2009).
21. M. M. Wolf, D. Perez-Garcia, C. Fernandez, Phys. Rev. Lett. 103, 230402 (2009).
22. A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic, Dordrecht, Netherlands, 1993).
23. In an XOR game, the answers a ∈ {0,1} and b ∈ {0,1} of Alice and Bob, respectively, are single bits; whether Alice and Bob win or not depends only on the XOR of the answers a ⊕ b = a + b mod 2.
24. The retrieval game used was discovered in collaboration with A. Doherty. Supported by the Royal Society ( J.O.) and by NSF grants PHY-04056720 and PHY-0803371, the National Research Foundation of Singapore, and the Singapore Ministry of Education (S.W.). Part of this work was done while J.O. was visiting California Institute of Technology, and while J.O. and S.W. were visiting the Kavli Institute for Theoretical Physics (Santa Barbara, CA), which is funded by NSF grant PHY-0551164.