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An entangled web of crime: Bell’s theorem as a short story
1.J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics (N.Y.) 1, 195–200 (1964),
1.reprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987).
2.For a review of experiments through 1987, see M. Redhead, Incompleteness, Nonlocality, and Realism (Clarendon, Oxford, 1987), pp. 107–113.
2.For many of the experiments through 1995, see A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Quantum optical tests of the foundations of physics,” in Atomic, Molecular, & Optical Physics Handbook (AIP, New York, 1996), pp. 907–909.
2.A. Aspect, P. Grangier, and G. Roger, “Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A new violation of Bell’s inequalities,” Phys. Rev. Lett. 49, 91–94 (1982).
3.C. Jack, “Sherlock Holmes investigates the EPR paradox,” Phys. World 8, 39–42 (1995).
4.H. Price, “A neglected route to realism about quantum mechanics,” Mind 103, 303–336 (1994);
4.Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time (Oxford University Press, Oxford, 1996).
5.R. Penrose, Shadows of the Mind (Oxford University Press, Oxford, 1996).
7.A. M. Steane and W. van Dam, “Physicists triumph at guess my number,” Phys. Today 53, 35–39 (2000).
10.D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem,” in Bell’s Theorem, Quantum Theory, and Conceptions of the Universe (Kluwer, Dordrecht, 1989), pp. 73–76.
11.N. D. Mermin, “Quantum mysteries revisited,” Am. J. Phys. 58, 731–734 (1990);
11.N. D. Mermin,“What’s wrong with these elements of reality?” Phys. Today 43(6), 9–11 (1990).
12.D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1143 (1990).
13.R. Clifton, M. Redhead, and J. Butterfield, “Generalization of the Greenberger-Horne-Zeilinger algebraic proof of nonlocality,” Found. Phys. 21, 149–184 (1991).
, A. Broadbent
, and A. Tapp
, “Quantum pseudo-telepathy
15.P. K. Aravind, “Bell’s theorem without inequalities and only two distant observers,” Found. Phys. Lett. 15, 397–405 (2002).
See also P. K. Aravind
, “A simple demonstration of Bell’s theorem involving two observers and no probabilities or inequalities
16.F. Laloë, “Do we really understand quantum mechanics? Strange correlations, paradoxes and theorems,” Am. J. Phys. 69, 655–701 (2001).
17.N. D. Mermin, “Spooky actions at a distance: Mysteries of the quantum theory,” in The Great Ideas Today 1988, Encyclopædia Britannica, pp. 2–53.
17.Reprinted in N. D. Mermin, Boojums All the Way Through: Communicating Science in a Prosaic Age (Cambridge University Press, Cambridge, 1990), Chap. 12.
18.H. Buhrman, R. Cleve, and A. Wigderson, “Quantum vs. classical communication and computation,” Proc. 30th ACM Symposium on Theory of Computing (1998), pp. 63–68.
19.In the first case we must know the no-cloning theorem, and in the second one we must know that a qubit can contain only one bit of information, despite being preparable in infinitely many different ways.
21.R. W. Spekkens
, “In defense of the epistemic view of quantum states: A toy theory
, and references therein.
22.H. Engel, Mr. Doyle and Dr. Bell (Overlook, New York, 2003).
23.D. Pirie, The Patient’s Eyes (St. Martin’s, New York, 2002);
23.The Night Calls (St. Martin’s, New York, 2003).
24.For readers who are familiar with Mermin’s illustration of nonlocality (Ref. 11), upon which the situation here is based, it may be helpful to note which elements of our scenario correspond to those of Mermin’s. The three clients in our story take the place of Mermin’s three detectors, and the two settings on these detectors to the two sides of each of the robbers (setting 1 to the back and setting 2 to the front). The four different combinations of detector settings therefore correspond to the four different combinations of sides of the robbers seen by the four guards. Finally, the two colors that the detectors can flash correspond to the same two colors of the robbers’ suits. Thus, in Mermin’s case when he sets the detector settings to 111, for example, and states that an even number of the three detectors flash red, that corresponds in our case to saying that the fourth guard saw an even number of the robbers wearing red.
26.Quant. Inf. Comp. 1, Special Issue on Implementation of Quantum Computation (2001).
27.T. Maudlin, Quantum Non-locality and Relativity (Blackwell, Oxford, 1994).
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