The mystery of the quantum cakes

American Journal of Physics

Volumn 68, Issue 1, 2000, Pages 33-36

  Kwiat, P G ^a   Hardy, L ^b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034421783     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19369     Document Type: Article

References (32)

1. E. Schrödinger, "Discussion of probability relations between separated systems," Proc. Cambridge Philos. Soc. 31, 555-563 (1935).
2. Other examples are the "collapse" of the wave function when a photon is detected in one or the other output port of a beamsplitter; and the Aharanov-Bohm effect, in which a particle "knows" about enclosed magnetic flux, even though the actual magnetic field can be strictly zero in all regions the particle traverses.
3. A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. A 47, 777-780 (1935).
4. J. S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics 1, 195-200 (1964), reprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge U.P., Cambridge, 1987).
5. J. S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics 1, 195-200 (1964), reprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge U.P., Cambridge, 1987).
6. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, "Proposed experiment to test local hidden-variable theories," Phys. Rev. Lett. 23, 880-884 (1969); J. F. Clauser and M. A. Home, "Experimental consequences of objective local theories," Phys. Rev. D 10, 526-535 (1974).
7. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, "Proposed experiment to test local hidden-variable theories," Phys. Rev. Lett. 23, 880-884 (1969); J. F. Clauser and M. A. Home, "Experimental consequences of objective local theories," Phys. Rev. D 10, 526-535 (1974).
8. J. F. Clauser and A. Shimony, "Bell's theorem: Experimental tests and implications, Rep" Prog. Phys. 41, 1881-1927 (1978).
9. See, for example, Ref. 6, for a review of experiments through 1977; M. Redhead, Incompleteness, Nonlocality, and Realism (Clarendon, Oxford, 1987), pp. 107-113, for experiments through 1987; A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, "Quantum optical tests of the foundations of physics," in the Atomic, Molecular, & Optical Physics Handbook (AIP Press, New York, 1996), pp. 907-909, for many of the tests through 1995; P. G. Kwiat et al., "New high intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995); D. V. Strekalov et al., "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-4 (1996); W. Tittel et al., "Violation of Bell inequalities by photons more than 10 km apart," Phys. Rev. Lett. 81, 3563-3566 (1998); and P. G. Kwiat et al., "Ultrabright source of polarization-entangled photons," Phys. Rev. A 60, R773-R776 (1999).
10. See, for example, Ref. 6, for a review of experiments through 1977; M. Redhead, Incompleteness, Nonlocality, and Realism (Clarendon, Oxford, 1987), pp. 107-113, for experiments through 1987; A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, "Quantum optical tests of the foundations of physics," in the Atomic, Molecular, & Optical Physics Handbook (AIP Press, New York, 1996), pp. 907-909, for many of the tests through 1995; P. G. Kwiat et al., "New high intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995); D. V. Strekalov et al., "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-4 (1996); W. Tittel et al., "Violation of Bell inequalities by photons more than 10 km apart," Phys. Rev. Lett. 81, 3563-3566 (1998); and P. G. Kwiat et al., "Ultrabright source of polarization-entangled photons," Phys. Rev. A 60, R773-R776 (1999).
11. See, for example, Ref. 6, for a review of experiments through 1977; M. Redhead, Incompleteness, Nonlocality, and Realism (Clarendon, Oxford, 1987), pp. 107-113, for experiments through 1987; A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, "Quantum optical tests of the foundations of physics," in the Atomic, Molecular, & Optical Physics Handbook (AIP Press, New York, 1996), pp. 907-909, for many of the tests through 1995; P. G. Kwiat et al., "New high intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995); D. V. Strekalov et al., "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-4 (1996); W. Tittel et al., "Violation of Bell inequalities by photons more than 10 km apart," Phys. Rev. Lett. 81, 3563-3566 (1998); and P. G. Kwiat et al., "Ultrabright source of polarization-entangled photons," Phys. Rev. A 60, R773-R776 (1999).
12. See, for example, Ref. 6, for a review of experiments through 1977; M. Redhead, Incompleteness, Nonlocality, and Realism (Clarendon, Oxford, 1987), pp. 107-113, for experiments through 1987; A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, "Quantum optical tests of the foundations of physics," in the Atomic, Molecular, & Optical Physics Handbook (AIP Press, New York, 1996), pp. 907-909, for many of the tests through 1995; P. G. Kwiat et al., "New high intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995); D. V. Strekalov et al., "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-4 (1996); W. Tittel et al., "Violation of Bell inequalities by photons more than 10 km apart," Phys. Rev. Lett. 81, 3563-3566 (1998); and P. G. Kwiat et al., "Ultrabright source of polarization-entangled photons," Phys. Rev. A 60, R773-R776 (1999).
13. See, for example, Ref. 6, for a review of experiments through 1977; M. Redhead, Incompleteness, Nonlocality, and Realism (Clarendon, Oxford, 1987), pp. 107-113, for experiments through 1987; A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, "Quantum optical tests of the foundations of physics," in the Atomic, Molecular, & Optical Physics Handbook (AIP Press, New York, 1996), pp. 907-909, for many of the tests through 1995; P. G. Kwiat et al., "New high intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995); D. V. Strekalov et al., "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-4 (1996); W. Tittel et al., "Violation of Bell inequalities by photons more than 10 km apart," Phys. Rev. Lett. 81, 3563-3566 (1998); and P. G. Kwiat et al., "Ultrabright source of polarization-entangled photons," Phys. Rev. A 60, R773-R776 (1999).
14. See, for example, Ref. 6, for a review of experiments through 1977; M. Redhead, Incompleteness, Nonlocality, and Realism (Clarendon, Oxford, 1987), pp. 107-113, for experiments through 1987; A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, "Quantum optical tests of the foundations of physics," in the Atomic, Molecular, & Optical Physics Handbook (AIP Press, New York, 1996), pp. 907-909, for many of the tests through 1995; P. G. Kwiat et al., "New high intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995); D. V. Strekalov et al., "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-4 (1996); W. Tittel et al., "Violation of Bell inequalities by photons more than 10 km apart," Phys. Rev. Lett. 81, 3563-3566 (1998); and P. G. Kwiat et al., "Ultrabright source of polarization-entangled photons," Phys. Rev. A 60, R773-R776 (1999).
15. Work is currently in progress at several institutions to perform a so-called "loophole-free" test of Bell's inequalities, that would not require the supplementary assumptions present in every experiment thus far. One remarkable exception is the recent experiment by G. Weihs et al. ["Violation of Bell's inequality under strict Einstein locality conditions," Phys. Rev. Lett. 81, 5039-5043 (1998)], in which all measurements were performed with truly space-like separations.
16. For example, N. D. Mermin, "Is the moon there when nobody looks? Reality and the quantum theory," Phys. Today, 38-47 (Apr. 1985); J. S. Bell, "Bertlmann's socks and the nature of reality," reprinted in J. S. Bell, in Ref. 4.
17. For example, N. D. Mermin, "Is the moon there when nobody looks? Reality and the quantum theory," Phys. Today, 38-47 (Apr. 1985); J. S. Bell, "Bertlmann's socks and the nature of reality," reprinted in J. S. Bell, in Ref. 4.
18. D. M. Greenberger, M. Horne, and A. Zeilinger, "Going beyond Bell's theorem," in Bell's Theorem, Quantum Theory, and Conceptions of the Universe (Kluwer, Dordrecht, The Netherlands, 1989), pp. 73-76;
19. D. M. Greenberger, M. Horne, A. Shimony, and A. Zeilinger, "Bell's theorem without inequalities," Am. J. Phys. 58, 1131-1143 (1990).
20. L. Hardy, "Nonlocality for two particles without inequalities for almost all entangled states," Phys. Rev. Lett. 71, 1665-1668 (1993).
21. T. F. Jordan, "Testing Einstein-Podolsky-Rosen assumptions without inequalities with 2 photons or particles with spin 1/2," Phys. Rev. A 50, 62-66 (1994).
22. N. D. Mermin, "Quantum mysteries refined," Am. J. Phys. 62, 880-887 (1994).
23. Of course, as has been pointed out by many authors (Refs. 13 and 15), any physical test (Refs. 16 and 17) of the Hardy logic will inevitably lead to an inequality (perhaps not surprisingly, it is a version of the original Bell inequality). For example, even in a perfect, noiseless system, one can never prove the nonexistence of a certain class of events to better than ∼ 1/N, where N is the number of times one looked for the event.
24. A. Garuccio, "Hardy's approach, Eberhard's inequality, and supplementary assumptions," Phys. Rev. A 52, 2535-2537 (1995).
25. J. R. Torgerson, D. Branning, C. H. Monken, and L. Mandel, "Experimental demonstration of the violation of local realism without Bell inequalities," Phys. Lett. A 204, 323-328 (1995); G. Digiuseppe, F. De Martini, and D. Boschi, "Experimental test of the violation of local realism in quantum-mechanics without Bell inequalities," Phys. Rev. A 56, 176-181 (1997); D. Boschi, S. Branca, F. De Martini, and L. Hardy, "Ladder proof of nonlocality without inequalities: Theoretical and experimental results," Phys. Rev. Lett. 79, 2755-2758 (1997).
26. J. R. Torgerson, D. Branning, C. H. Monken, and L. Mandel, "Experimental demonstration of the violation of local realism without Bell inequalities," Phys. Lett. A 204, 323-328 (1995); G. Digiuseppe, F. De Martini, and D. Boschi, "Experimental test of the violation of local realism in quantum-mechanics without Bell inequalities," Phys. Rev. A 56, 176-181 (1997); D. Boschi, S. Branca, F. De Martini, and L. Hardy, "Ladder proof of nonlocality without inequalities: Theoretical and experimental results," Phys. Rev. Lett. 79, 2755-2758 (1997).
27. J. R. Torgerson, D. Branning, C. H. Monken, and L. Mandel, "Experimental demonstration of the violation of local realism without Bell inequalities," Phys. Lett. A 204, 323-328 (1995); G. Digiuseppe, F. De Martini, and D. Boschi, "Experimental test of the violation of local realism in quantum-mechanics without Bell inequalities," Phys. Rev. A 56, 176-181 (1997); D. Boschi, S. Branca, F. De Martini, and L. Hardy, "Ladder proof of nonlocality without inequalities: Theoretical and experimental results," Phys. Rev. Lett. 79, 2755-2758 (1997).
28. A. G. White et al., "Non-maximally entangled states: production, characterization, and utilization," Phys. Rev. Lett. (to appear, 1999); see also the last article in Ref. 7.
29. N. D. Mermin, "The best version of Bell's Theorem," in Fundamental Problems in Quantum Theory [Ann. (N.Y.) Acad. Sci. 755, 616-623 (1995)].
30. S. Popescu and D. Rohrlich, "Quantum nonlocality as an axiom," Found. Phys. 24, 379-385 (1994).
31. The probabilities of the various results at the 50% threshold are P(R,R) = P(N,N) = P(G,B) = P(B,G) = P(R,G) = P(N,B) = P(G,R) = P(B,N) = 1/2, with all other possibilities zero ("R", "N", "G", and "B" stand for Risen, Not Risen, Good, and Bad, respectively); clearly, with these probabilities no measurements performed on one side can reveal the type of measurement performed by the other experimenter.
32. One example would have P(R,R) = P(R,G) = P(G,R) = P(G,B) = 1, and all other probabilities zero. Here, Lucy's cakes always Rise early and always taste Good, independent of Ricardo's measurement, and Ricardo only has Risen cakes; but the taste of his cakes is completely determined by Lucy's type of measurement. For the case P(R,R) = P(R,G) = P(G,R) = 1; P(G,B) = P(B,G) = 12; and all other probabilities zero, the nonlocality shows up in the tastes of both parties' cakes, but not deterministically, i.e., tasting a single cake would not necessarily reveal whether the "sender" had measured in the middle or the end.