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Summary
Proposed by Einstein, Podolsky, and Rosen (EPR) in 1935, the entangled state has played a central part in exploring the foundation of quantum mechanics. At the end of the twentieth century, however, some physicists and mathematicians set aside the epistemological debates associated with EPR and turned it from a philosophical puzzle into practical resources for information processing. This paper examines the origin of what is known as quantum information. Scientists had considered making quantum computers and employing entanglement in communications for a long time. But the real breakthrough only occurred in the 1980s when they shifted focus from general-purpose systems such as Turing machines to algorithms and protocols that solved particular problems, including quantum factorization, quantum search, superdense code, and teleportation. Key to their development was two groups of mathematical manipulations and deformations of entanglement—quantum parallelism and ‘feedback EPR’—that served as conceptual templates. The early success of quantum parallelism and feedback EPR was owed to the idealized formalism of entanglement researchers had prepared for philosophical discussions. Yet, such idealization is difficult to hold when the physical implementation of quantum information processors is at stake. A major challenge for today's quantum information scientists and engineers is thus to move from Einstein et al.'s well-defined scenarios into realistic models.
Acknowledgements
An earlier version of this article appeared as Chen-Pang Yeang, ‘Engineering the entanglement: quantum computation, quantum communication, and re-conceptualizing information’, in HQ1: Conference on the History of Quantum Physics, edited by Christian Joas, Christoph Lehner, and Jürgen Renn (Preprint #350, Max Planck Institute for the History of Science, Berlin: 2008), 345–65. The author also wishes to express his gratitude to an anonymous referee of this journal for the very useful advice regarding the historical discussion on the research into the foundation of quantum mechanics.
Notes
1For the Historical works on the Einstein–Bohr dabate and the EPR thought experiment, see, e.g., Arthur Fine, The Shaky Game: Einstein, Realism, and the Quantum Theory (Chicago: University of Chicago press, 1986), ch. 3; Mara Beller and Arthur Fine, ‘Bohr's response to EPR’, in Niels Bohr and contemporary Philosophy, edited by Jan Faye and Henry Folse (Dordrecht: Kluwer, 1994), 1–31; Mara Beller, Quantum Dialogue: The Making of a Revolution (Chicago: University of Chicago Press, 1999), 145–70.
2The wave function is . See Albert Einstein, Boris Podolsky, and Nathan Rosen, ‘Can quantum-mechanical description of physical reality be considered complete?’, Physical Review, 47 (1935), 779, equation (10).
3The wave function is . See Albert Einstein, Boris Podolsky, and Nathan Rosen, ‘Can quantum-mechanical description of physical reality be considered complete?’, Physical Review, 47 (1935), 779, equation (10)., 777–80.
4During the late 1930s and 1940s, the general consensus among physicists was that the issues concerning the foundation of quantum mechanics, in which EPR was part of the discussion, had been resolved by Bohr, Heisenberg, Pauli, and von Neumann. The situation changed in 1950–70 as several ‘dissidents’—including David Bohm, John Bell, Eugene Wigner, and Hugh Everett—came to challenge or reinterpret the standard Copenhagen interpretation in various ways. See Olival Freire, Jr, ‘The historical roots of “foundations of quantum physics” as a field of research (1950–70)’, Foundations of Physics, 34:11 (2004), 1741–60.
5David Bohm, Quantum Theory (New York: Dover, 1951), 611–19. Also see David Bohm and Yakir Aharonov, ‘Discussion of experimental proof for the paradox of Einstein, Rosen, and Podolsky’, Physical Review, 108:4 (1957), 1070–6.
6John S. Bell, ‘On the Einstein–Podolsky–Rosen paradox’, Physics 1 (1964), 195–200; reprinted in John S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy (Cambridge: Cambridge University Press, 2004), 14–21. More precisely, Bell demonstrated that Bohm's hidden-variable theory did not contradict von Neumann's proof against hidden variables, because von Neumann referred to local hidden variables yet Bohm's variables were non-local. See John Bell, ‘On the problem of hidden variables in quantum mechanics’, Review of Modern Physics, 38:3 (1966), 447–52. For a more popular account of Bell's work, see David Mermin, ‘Quantum mysteries for anyone’, Journal of Philosophy, 78 (1981), 397–408.
7Olival Freire, Jr, ‘Quantum dissidents: research on the foundations of quantum theory circa 1970’, Studies in History and Philosophy of Modern Physics, 40 (2009), 280–9; Freire, ‘The historical root’ (2004), 1741–60; Joan Lisa Bromberg, ‘Device physics vis-à-vis fundamental physics in Cold War America: the case of quantum optics’, Isis, 97:2 (2006), 237–59. Freire and Bromberg hold different views on the cause of the turning point circa 1970. Bromberg claims that the significant increase in research on Bell's theory was enabled by the availability of experimental techniques and instruments in quantum optics, which made it possible to implement entanglement and test the Bell inequality in laboratory. Freire argues that the changing material culture constituted only part of the cause. The turning point should also be seen as the accumulative product of a 20-year-long cultural movement that attempted to alter physicists’ general attitudes toward the forbidden topics in the foundations of quantum physics. For the Bohmian and Bellian philosophical deliberations on quantum mechanics, especially their refutation of the Copenhagen interpretation, see, e.g. James Cushing, ‘A Bohmian response to Bohr's complementarity’, in Niels Bohr and Contemporary Philosophy, edited by Faye and Folse (1994), 57–750; James Cushing, Quantum Mechanics, Historical Contingency and the Copenhagen Hegemony (Chicago: University of Chicago Press, 1994); Bell, Speakable and Unspeakable in Quantum Mechanics (1994). For more general discussions on the philosophy of quantum mechanics, see, e.g. Michael Readhead, Incompleteness, Nonlocality and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics (Oxford: Clarendon Press, 1989).
8For engineering knowledge, see Walter Vincenti, What Engineers Know and How They Know It (Baltimore: Johns Hopkins University Press, 1990).
9Alan Turing, ‘On computable numbers, with an application to the Entscheidungsproblem’, Proceedings of the London Mathematical Society, series 2, 42 (1936–37), 230–65; Alonzo Church, ‘An unsolvable problem of elementary number theory’, American Journal of Mathematics, 58 (1936), 345–63.
10For a brief historical overview of the physics of computation, see Michael Nielsen and Isaac Chuang, Quantum Computation and Quantum Information (Cambridge: Cambridge University Press, 2000), 167–8.
11Charles Bennett, ‘Logical reversibility of computation’, IBM Journal of Research and Development, 17:6 (1973), 525–32; Edward Fredkin and Tommaso Toffoli, ‘Conservative logic’, International Journal of Theoretical Physics, 21:3/4 (1982), 219–53.
12For a brief review of the literature on quantum computing before 1980, see Paul Benioff, ‘The computer as a physical system: a microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines’, Journal of Statistical Physics, 22:5 (1980), 563–66.
13Paul Benioff, ‘Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: application to Turing machines’, International Journal of Theoretical Physics, 21:3/4 (1982), 177–201.
14Richard Feynman, ‘Simulating physics with computers’, International Journal of Theoretical Physics, 21:6/7 (1982), 467.
15Richard Feynman, ‘Simulating physics with computers’, International Journal of Theoretical Physics, 21:6/7 (1982), 467., 476–85. Alt hough Feynman did not cite works on the violation of the Bell inequality, his example nonetheless clearly referred to that inequality. Thus he was earlier than Deutsch to make the connection between quantum computation and the EPR state/Bell inequality. However, Feynman's connection here had nothing to do with exploiting the computational advantage of the EPR state, as Deutsch's did. Instead, Feynman's sole point was that classical computers are incapable of simulating a quantum system because of its entangled nature; we have to use quantum computers for that purpose.
16Richard Feynman, ‘Simulating physics with computers’, International Journal of Theoretical Physics, 21:6/7 (1982), 467., 476–85. Alt hough Feynman did not cite works on the violation of the Bell inequality, his example nonetheless clearly referred to that inequality. Thus he was earlier than Deutsch to make the connection between quantum computation and the EPR state/Bell inequality. However, Feynman's connection here had nothing to do with exploiting the computational advantage of the EPR state, as Deutsch's did. Instead, Feynman's sole point was that classical computers are incapable of simulating a quantum system because of its entangled nature; we have to use quantum computers for that purpose., 474–6.
17Filiz Peach's interview with David Deutsch in Philosophy Now, 30 December 2000 (http://www.qubit.org/people/david/Articles/PhilosophyNow.html); ‘David Deutsch’, in Edge: The Third Culture (http://www.edge.org/3rd_culture/bios/deutsch.html).
18David Deutsch, ‘Quantum theory, the Church–Turing principle, and the universal quantum computer’, Proceedings of the Royal Society of London A, 400:1818 (1985), 97–107.
19David Deutsch, ‘Quantum theory, the Church–Turing principle, and the universal quantum computer’, Proceedings of the Royal Society of London A, 400:1818 (1985), 97–107., 111–13.
20David Deutsch, ‘Quantum theory, the Church–Turing principle, and the universal quantum computer’, Proceedings of the Royal Society of London A, 400:1818 (1985), 97–107., 112.
21David Deutsch, ‘Quantum computational networks’, Proceedings of the Royal Society of London A, 425:1868 (1989), 73–90.
22Benjamin Schumacher, ‘Quantum coding’, Physical Review A, 51:4 (1995), 2747.
23Mathematics Genealogy Project, North Dakota State University: http://genealogy.math.ndsu.nodak. edu/id.php?id=99574.
24David Deutsch and Richard Jozsa, ‘Rapid solutions of problems by quantum computation’, Proceedings of the Royal Society of London A, 439:1907 (1992), 553–8.
25Department of Mathematics, MIT: ht tp://www-math.mit.edu/~shor/pubs.html.
26Peter Shor, ‘Algorithms for quantum computation: discrete logarithms and factoring’, Proceedings of the 35th Annual Symposium on Foundations of Computer Science (1994), 124–34.
27Nielsen and Chuang, Quantum Computation (2000), 226.
28Shor, ‘Logarithms and factoring’ (1994), 127–8.
29Shor, ‘Logarithms and factoring’ (1994), 127–8., 128–9.
30For RSA, see Kenneth Rosen, Elementary Number Theory and Its Applications (Reading, MA: Addison-Wesley, 1988), 231–5.
31For RSA, see Kenneth Rosen, Elementary Number Theory and Its Applications (Reading, MA: Addison-Wesley, 1988), 231–5., 130–3; Peter Shor, ‘Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer’, SIAM Journal of Computing, 26:5 (1997), 1484–509.
32For Grover's early publications on optimization, see, e.g. Lov Grover, ‘Standard cell placement using simulated sintering’, Proceedings of the 24th ACM/IEEE Design Automation Conference (1987), 56–9; Sivanarayana Mallela and Lov Grover, ‘Clustering based simulated annealing for standard cell placement’, Proceedings of the 25th ACM/IEEE Design Automation Conference (1988), 312–17; Lov Grover, ‘Local search and the local structure of NP-complete problems’, Operations Research Letter, 12 (1992), 235–43.
33Lov Grover, ‘A fast quantum mechanical algorithm for database search’, Proceedings of 28th Annual ACM Symposium on Theory of Computing (STOC) (1996), 212–19.
34Lov Grover, ‘Quantum mechanics helps in searching for a needle in a haystack’, Physical Review Letters, 79:2 (1997), 325–8.
35Lov Grover, ‘Quantum mechanics helps in searching for a needle in a haystack’, Physical Review Letters, 79:2 (1997), 325–8., 325.
36Lov Grover, ‘Quantum mechanics helps in searching for a needle in a haystack’, Physical Review Letters, 79:2 (1997), 325–8., 326–8.
37For this historical connection, see William Aspray, ‘The scientific conceptualization of information: a survey’, Annals for the History of Computing, 7:2 (1985), 117–40.
38A classical argument against the superluminal effect is in A. Shimony, ‘Controllable and uncontrollable non-locality’, Proceedings of the International Symposium on the Foundation of Quantum Mechanics (Tokyo: Komuyama Printing Co., 1984), 225–30. Also, see P. H. Eberhard, ‘Bell's theorem and the different concepts of locality’, Il Nuovo Cimento, 46B:2 (1978), 392–419; G. C. Ghirardi, A. Rimini, and T. Weber, ‘A general argument against superluminal transmission through quantum mechanical measurement process’, Lettere al Nuovo Cimento, 27:10 (1980), 293–8; and D. N. Page, ‘The Einstein–Podolsky–Rosen physical reality is completely described by quantum mechanics’, Physics Letters, 91A:2 (1982), 57–60.
39IBM Research Center: http://www.research.ibm.com/people/b/bennetc/chbbio.html.
40Alain Aspect, Phillipe Grangier, and Gérard Roger, ‘Experimental realization of Einstein–Podolsky–Rosen–Bohm Gedanken experiment: a new violation of Bell's inequalities’, Physical Review Letters, 49:2 (1982), 91–4; Alain Aspect, Jean Dalibard, and Gérard Roger, ‘Experimental tests of Bell's inequalities using variable analysis’, Physical Review Letters, 49:25 (1982), 1804–7; M. A. Horne and Anton Zeilinger, ‘Einstein–Podolsky–Rosen interferometry, new techniques and ideas in quantum measurement theory’, in Annals of the New York Academy of Sciences, 480, edited by D. Greenberger (1986), 469. For a historical review of the early EPR experiments, see Olival Freire, Jr, ‘Philosophy enters the optics laboratory: Bell's theorem and its first experimental tests (1965–1982)’, Studies in History and Philosophy of Modern Physics, 37 (2006), 577–616.
41Stephen Wiesner, ‘Conjugate coding’, SIGACT News, 15 (1983), 77.
42Charles Bennett and Gilles Brassard, ‘Quantum cryptography: public key distribution and coin tossing’, Proceedings of IEEE International Conference on Computer Systems and Signal Processing (Bangalore, India, December 1984), 175–9.
43 http://www.research.ibm.com/people/b/bennetc/chbbio.html; Charles Bennett and Gilles Brassard , ‘The dawn of a new era in quantum cryptography: the experimental prototype is working’, ACM SIGACT News, 20 (1989), 78–83.
44Shimony, ‘Controllable and uncontrollable non-locality’ (1984), 225–30.
45Charles Bennett and Stephen Wiesner, ‘Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states’, Physical Review Letters, 69:16 (1992), 2881–4.
46Charles Bennett, Gilles Brassard, C. Crepeau, Richard Jozsa, A. Peres, and W. Wootters, ‘Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels’, Physical Review Letters, 70:13 (1993), 1895–9.
47Eric Hand, ‘Enlisting investigators’, Nature, 466 (29 July 2010), 656–7.
48Home page of the Institute for Quantum Computing, University of Waterloo (http://new.iqc.ca/institute).
49Home page of QUROPE (http://qurope.eu/)
50Quantiki, Encyclopedia of quantum information: http://www.quantiki.org/wiki/Who%27s_Who_in_Quantum_Information.
51D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, ‘Experimental quantum teleportation’, Nature, 390:6660 (1997), 575–9; D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, ‘Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels’, Physical Review Letters, 80:6 (1998), 1121–5; A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, ‘Unconditional quantum teleportation’, Science, 282 (1998), 706–9.
52Freire, ‘Philosophy enters the optics laboratory’ (2006), 577–616.
53The ion trap was invented in the 1970s by the German atomic physicists Hans Dehmelt and Wolfgang Paul. See Nobel Prize website: http://nobelprize.org/nobel_prizes/physics/laureates/1989/index.html. The ion trap utilized an electromagnetic field to confine charged particles within a small volume. It was originally used in studies of atoms or smaller elementary particles, and hence was more familiar to atomic physicists and particle physicists. This technique was brought to quantum computing, because it offered a means to prepare and manipulate atomic particles at simple quantum states.
54A famous example is Peter Shor, ‘Fault-tolerant quantum computation’, Proceedings of the 37th Annual Symposium on Foundations of Computer Science (1996), 56–65. Also see Nielsen and Chuang, Quantum Computation (2000), 425–99.
55Rolf Landauer, IBM's chief physicist of computation, considered by many a godfather of quantum computation, once suggested that all papers on quantum computing should carry a footnote: ‘This proposal, like all proposals for quantum computation, relies on speculative technology, does not in its current form take into account all possible sources of noise, unreliability and manufacturing error, and probably will not work’. Seth Lloyd, ‘Obituary: Rolf Landauer (1927–99)’, Nature, 400:6746 (1999), 720.