Abstract

We report the experimental realization of a quantum analog of the classical Galton quincunx and discuss its possible use as a device for quantum computation. Our quantum quincunx is implemented with linear optical elements that allow an incoming photon to interfere with itself while traversing all possible paths from the source to the detector. We show that the experimentally determined intensity distributions are in excellent agreement with theory.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Aharonov, L. Davidovich, and N. Zagury, "Quantum random walks," Phys. Rev. A 48, 1687-1690 (1993).
    [CrossRef] [PubMed]
  2. T. D. Mackay, S. D. Bartlett, L. T. Stephenson, and B. C. Sanders, "Quantum walks in higher dimensions," J. Phys. A 35, 2745-2753 (2002).
    [CrossRef]
  3. B. C. Travaglione and G. J. Milburn, "Implementing the quantum random walk," Phys. Rev. A 65, 032310 (2002).
    [CrossRef]
  4. M. Bednarska, A. Grudkà, P. Kurzynski, T. Luczak, and A. Wojcik, "Quantum walks on cycles," Phys. Lett. A 317, 21-25 (2003).
    [CrossRef]
  5. B. C. Sanders, S. D. Bartlett, B. Tregenna, and P. L. Knight, "Quantum quincunx in cavity quantum electrodynamics," e-print quant-ph/0207028, http://www.arxiv.org/abs/quant-ph?0207028.
  6. A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman, "Exponential algorithmic speedup by quantum walk," e-print quant-ph/0209131, http://www.arxiv.org/abs/quant-ph?0209131.
  7. A. M. Childs, E. Farhi, and S. Gutmann, "An example of the difference between quantum and classical random walks," e-print quant-ph/0103020, http://www.arxiv.org/abs/quant-ph?0103020.
  8. A. Nayak and A. Vishwanath, "Quantum walk on the line," e-print quant-ph/0010117, http://www.arxiv.org/abs/quant-ph?0010117.
  9. D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, "Quantum walks on graphs," e-print quant-ph/0012090, http://www.arxiv.org/abs/quant-ph?0012090.
  10. Z. Zhao, J. Du, H. Li, T. Yang, Z.-B. Chen, and J.-W. Pan, "Implement quantum random walks with linear optics elements," e-print quant-ph/0212149, http://www.arxiv.org/abs/quant-ph?0212149.
  11. W. Dur, R. Raussendorf, V. M. Kendon, and H.-J. Briegel, "Quantum random walks in optical lattices," e-print quant-ph/0207137, http://www.arxiv.org/abs/quant-ph?0207137.
  12. F. Galton, "Typical laws of heredity," Nature 15, 492-495 , 512-514, 532-533 (1877).
    [CrossRef]
  13. M. L. Stohler, "Quantum game theory," Ph.D. thesis (Purdue University, West Lafayette, Ind.), manuscript available from the author.
  14. D. P. Divincenzo, "Quantum computation," Science 270, 255-261 (1995).
    [CrossRef]
  15. C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature 404, 247-255 (2000).
    [CrossRef] [PubMed]
  16. J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
    [CrossRef] [PubMed]
  17. T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, "Experimental controlled-NOT logic gate for single photons in the coincidence basis," Phys. Rev. A 68, 032316 (2003).
    [CrossRef]
  18. L. K. Grover, "Quantum mechanics helps in searching for a needle in a haystack," Phys. Rev. Lett. 79, 325-328 (1997).
    [CrossRef]
  19. D. Deutsch and R. Jozsa, "Rapid solution of problems by quantum computation," Proc. R. Soc. London 439, 553-558 (1992).
    [CrossRef]
  20. J. Preskill, "Quantum information and computation," Caltech Lecture Notes, http://www.theory.caltech.edu/people/preskill/ph229/lecture, Sec. 6.
  21. P. W. Shor, "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer," SIAM J. Comput. 26, 1484-1509 (1997).
    [CrossRef]
  22. E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
    [CrossRef] [PubMed]
  23. F. De Martini, V. Buzek, F. Sciarrino, and C. Sias, "Experimental realization of the quantum universal NOT gate," Nature 419, 815-818 (2002).
    [CrossRef] [PubMed]
  24. P. G. Kwiat, J. R. Mitchell, P. D. D. Schwindt, and A. G. White, "Grover's search algorithm: an optical approach," J. Mod. Opt. 47, 257-266 (2000).
    [CrossRef]
  25. S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
    [CrossRef] [PubMed]
  26. C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
    [CrossRef] [PubMed]
  27. I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd, "Experimental realization of a quantum algorithm," Nature 393, 143-146 (1998).
    [CrossRef]
  28. N. Linden, H. Barjat, and R. Freeman, "An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer," Chem. Phys. Lett. 296, 61-67 (1998).
    [CrossRef]
  29. L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, "Experimental realization of an order-finding algorithm with an NMR quantum computer," Phys. Rev. Lett. 85, 5452-5455 (2000).
    [CrossRef]
  30. J. A. Jones and M. Mosca, "Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer," J. Chem. Phys. 109, 1648-1653 (1998).
    [CrossRef]
  31. I. L. Chuang, N. Gershenfeld, and M. Kubinec, "Experimen-tal implementation of fast quantum searching," Phys. Rev. Lett. 80, 3408-3411 (1998).
    [CrossRef]
  32. J. A. Jones, M. Mosca, and R. H. Hansen, "Implementation of a quantum search algorithm on a quantum computer," Nature 393, 344-346 (1998).
    [CrossRef]
  33. M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
    [CrossRef] [PubMed]
  34. A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003).
    [CrossRef] [PubMed]
  35. A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, "Stimulated emission of polarization-entangled photons," Nature 412, 887-890 (2001).
    [CrossRef] [PubMed]
  36. W. Dur, R. Raussendorf, V. M. Kendon, and H.-J. Briegel, "Quantum random walks in optical lattices," e-print quant-ph/0207137, http://www.arxiv.org/abs/quant-ph?0207137.
  37. D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, "Quantum walks on graphs," e-print quant-ph/0012090, http://www.arxiv.org/abs/quant-ph?0012090.
  38. A. M. Childs, R. Cleve, E. Deotto, E. Fahri, S. Gutmann, and D. A. Spielman, "Exponential algorithmic speedup by quantum walk," e-print quant-ph/0209131, http://www.arxiv.org/abs/quant-ph?0209131.

2003

M. Bednarska, A. Grudkà, P. Kurzynski, T. Luczak, and A. Wojcik, "Quantum walks on cycles," Phys. Lett. A 317, 21-25 (2003).
[CrossRef]

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, "Experimental controlled-NOT logic gate for single photons in the coincidence basis," Phys. Rev. A 68, 032316 (2003).
[CrossRef]

S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
[CrossRef] [PubMed]

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003).
[CrossRef] [PubMed]

2002

F. De Martini, V. Buzek, F. Sciarrino, and C. Sias, "Experimental realization of the quantum universal NOT gate," Nature 419, 815-818 (2002).
[CrossRef] [PubMed]

T. D. Mackay, S. D. Bartlett, L. T. Stephenson, and B. C. Sanders, "Quantum walks in higher dimensions," J. Phys. A 35, 2745-2753 (2002).
[CrossRef]

B. C. Travaglione and G. J. Milburn, "Implementing the quantum random walk," Phys. Rev. A 65, 032310 (2002).
[CrossRef]

2001

A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, "Stimulated emission of polarization-entangled photons," Nature 412, 887-890 (2001).
[CrossRef] [PubMed]

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
[CrossRef] [PubMed]

2000

L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, "Experimental realization of an order-finding algorithm with an NMR quantum computer," Phys. Rev. Lett. 85, 5452-5455 (2000).
[CrossRef]

P. G. Kwiat, J. R. Mitchell, P. D. D. Schwindt, and A. G. White, "Grover's search algorithm: an optical approach," J. Mod. Opt. 47, 257-266 (2000).
[CrossRef]

C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature 404, 247-255 (2000).
[CrossRef] [PubMed]

1998

J. A. Jones and M. Mosca, "Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer," J. Chem. Phys. 109, 1648-1653 (1998).
[CrossRef]

I. L. Chuang, N. Gershenfeld, and M. Kubinec, "Experimen-tal implementation of fast quantum searching," Phys. Rev. Lett. 80, 3408-3411 (1998).
[CrossRef]

J. A. Jones, M. Mosca, and R. H. Hansen, "Implementation of a quantum search algorithm on a quantum computer," Nature 393, 344-346 (1998).
[CrossRef]

I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd, "Experimental realization of a quantum algorithm," Nature 393, 143-146 (1998).
[CrossRef]

N. Linden, H. Barjat, and R. Freeman, "An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer," Chem. Phys. Lett. 296, 61-67 (1998).
[CrossRef]

1997

P. W. Shor, "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer," SIAM J. Comput. 26, 1484-1509 (1997).
[CrossRef]

L. K. Grover, "Quantum mechanics helps in searching for a needle in a haystack," Phys. Rev. Lett. 79, 325-328 (1997).
[CrossRef]

1995

D. P. Divincenzo, "Quantum computation," Science 270, 255-261 (1995).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

1993

Y. Aharonov, L. Davidovich, and N. Zagury, "Quantum random walks," Phys. Rev. A 48, 1687-1690 (1993).
[CrossRef] [PubMed]

1992

D. Deutsch and R. Jozsa, "Rapid solution of problems by quantum computation," Proc. R. Soc. London 439, 553-558 (1992).
[CrossRef]

1877

F. Galton, "Typical laws of heredity," Nature 15, 492-495 , 512-514, 532-533 (1877).
[CrossRef]

Aharonov, Y.

Y. Aharonov, L. Davidovich, and N. Zagury, "Quantum random walks," Phys. Rev. A 48, 1687-1690 (1993).
[CrossRef] [PubMed]

Aspelmeyer, M.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Barjat, H.

N. Linden, H. Barjat, and R. Freeman, "An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer," Chem. Phys. Lett. 296, 61-67 (1998).
[CrossRef]

Bartlett, S. D.

T. D. Mackay, S. D. Bartlett, L. T. Stephenson, and B. C. Sanders, "Quantum walks in higher dimensions," J. Phys. A 35, 2745-2753 (2002).
[CrossRef]

Becher, C.

S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
[CrossRef] [PubMed]

Bednarska, M.

M. Bednarska, A. Grudkà, P. Kurzynski, T. Luczak, and A. Wojcik, "Quantum walks on cycles," Phys. Lett. A 317, 21-25 (2003).
[CrossRef]

Bennett , C. H.

C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature 404, 247-255 (2000).
[CrossRef] [PubMed]

Blatt, R.

S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
[CrossRef] [PubMed]

Boca, A.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003).
[CrossRef] [PubMed]

Bohm, H. R.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Boozer, A. D.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003).
[CrossRef] [PubMed]

Bouwmeester, D.

A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, "Stimulated emission of polarization-entangled photons," Nature 412, 887-890 (2001).
[CrossRef] [PubMed]

Bowen, W. P.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003).
[CrossRef] [PubMed]

Branning, D.

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

Breyta, G.

L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, "Experimental realization of an order-finding algorithm with an NMR quantum computer," Phys. Rev. Lett. 85, 5452-5455 (2000).
[CrossRef]

Buzek, V.

F. De Martini, V. Buzek, F. Sciarrino, and C. Sias, "Experimental realization of the quantum universal NOT gate," Nature 419, 815-818 (2002).
[CrossRef] [PubMed]

Chou, C. W.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003).
[CrossRef] [PubMed]

Chuang, I. L.

S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
[CrossRef] [PubMed]

L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, "Experimental realization of an order-finding algorithm with an NMR quantum computer," Phys. Rev. Lett. 85, 5452-5455 (2000).
[CrossRef]

I. L. Chuang, N. Gershenfeld, and M. Kubinec, "Experimen-tal implementation of fast quantum searching," Phys. Rev. Lett. 80, 3408-3411 (1998).
[CrossRef]

I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd, "Experimental realization of a quantum algorithm," Nature 393, 143-146 (1998).
[CrossRef]

Cleve, R.

L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, "Experimental realization of an order-finding algorithm with an NMR quantum computer," Phys. Rev. Lett. 85, 5452-5455 (2000).
[CrossRef]

Davidovich, L.

Y. Aharonov, L. Davidovich, and N. Zagury, "Quantum random walks," Phys. Rev. A 48, 1687-1690 (1993).
[CrossRef] [PubMed]

De Martini, F.

F. De Martini, V. Buzek, F. Sciarrino, and C. Sias, "Experimental realization of the quantum universal NOT gate," Nature 419, 815-818 (2002).
[CrossRef] [PubMed]

Deutsch , D.

D. Deutsch and R. Jozsa, "Rapid solution of problems by quantum computation," Proc. R. Soc. London 439, 553-558 (1992).
[CrossRef]

DiVincenzo, D. P.

C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature 404, 247-255 (2000).
[CrossRef] [PubMed]

D. P. Divincenzo, "Quantum computation," Science 270, 255-261 (1995).
[CrossRef]

Duan, L. M.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003).
[CrossRef] [PubMed]

Eschner, J.

S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
[CrossRef] [PubMed]

Fitch, M. J.

T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, "Experimental controlled-NOT logic gate for single photons in the coincidence basis," Phys. Rev. A 68, 032316 (2003).
[CrossRef]

Franson, J. D.

T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, "Experimental controlled-NOT logic gate for single photons in the coincidence basis," Phys. Rev. A 68, 032316 (2003).
[CrossRef]

Freeman, R.

N. Linden, H. Barjat, and R. Freeman, "An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer," Chem. Phys. Lett. 296, 61-67 (1998).
[CrossRef]

Galton, F.

F. Galton, "Typical laws of heredity," Nature 15, 492-495 , 512-514, 532-533 (1877).
[CrossRef]

Gershenfeld, N.

I. L. Chuang, N. Gershenfeld, and M. Kubinec, "Experimen-tal implementation of fast quantum searching," Phys. Rev. Lett. 80, 3408-3411 (1998).
[CrossRef]

Grover, L. K.

L. K. Grover, "Quantum mechanics helps in searching for a needle in a haystack," Phys. Rev. Lett. 79, 325-328 (1997).
[CrossRef]

Grudkà, A.

M. Bednarska, A. Grudkà, P. Kurzynski, T. Luczak, and A. Wojcik, "Quantum walks on cycles," Phys. Lett. A 317, 21-25 (2003).
[CrossRef]

Gulde, S.

S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
[CrossRef] [PubMed]

Gyatso, T.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Haffner, H.

S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
[CrossRef] [PubMed]

Hansen, R. H.

J. A. Jones, M. Mosca, and R. H. Hansen, "Implementation of a quantum search algorithm on a quantum computer," Nature 393, 344-346 (1998).
[CrossRef]

Howell, J. C.

A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, "Stimulated emission of polarization-entangled photons," Nature 412, 887-890 (2001).
[CrossRef] [PubMed]

Itano, W. M.

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

Jacobs, B. C.

T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, "Experimental controlled-NOT logic gate for single photons in the coincidence basis," Phys. Rev. A 68, 032316 (2003).
[CrossRef]

Jennewein, T.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Jones, J. A.

J. A. Jones, M. Mosca, and R. H. Hansen, "Implementation of a quantum search algorithm on a quantum computer," Nature 393, 344-346 (1998).
[CrossRef]

Jones , J. A.

J. A. Jones and M. Mosca, "Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer," J. Chem. Phys. 109, 1648-1653 (1998).
[CrossRef]

Jozsa, R.

D. Deutsch and R. Jozsa, "Rapid solution of problems by quantum computation," Proc. R. Soc. London 439, 553-558 (1992).
[CrossRef]

Kaltenbaek, R.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Kimble, H. J.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003).
[CrossRef] [PubMed]

King, B. E.

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
[CrossRef] [PubMed]

Kubinec, M.

I. L. Chuang, N. Gershenfeld, and M. Kubinec, "Experimen-tal implementation of fast quantum searching," Phys. Rev. Lett. 80, 3408-3411 (1998).
[CrossRef]

Kurzynski, P.

M. Bednarska, A. Grudkà, P. Kurzynski, T. Luczak, and A. Wojcik, "Quantum walks on cycles," Phys. Lett. A 317, 21-25 (2003).
[CrossRef]

Kuzmich, A.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003).
[CrossRef] [PubMed]

Kwiat, P. G.

P. G. Kwiat, J. R. Mitchell, P. D. D. Schwindt, and A. G. White, "Grover's search algorithm: an optical approach," J. Mod. Opt. 47, 257-266 (2000).
[CrossRef]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
[CrossRef] [PubMed]

Lamas-Linares, A.

A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, "Stimulated emission of polarization-entangled photons," Nature 412, 887-890 (2001).
[CrossRef] [PubMed]

Lancaster, G. P.

S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
[CrossRef] [PubMed]

Leung, D. W.

I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd, "Experimental realization of a quantum algorithm," Nature 393, 143-146 (1998).
[CrossRef]

Linden, N.

N. Linden, H. Barjat, and R. Freeman, "An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer," Chem. Phys. Lett. 296, 61-67 (1998).
[CrossRef]

Lindenthal, M.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Lloyd, S.

I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd, "Experimental realization of a quantum algorithm," Nature 393, 143-146 (1998).
[CrossRef]

Luczak, T.

M. Bednarska, A. Grudkà, P. Kurzynski, T. Luczak, and A. Wojcik, "Quantum walks on cycles," Phys. Lett. A 317, 21-25 (2003).
[CrossRef]

Mackay, T. D.

T. D. Mackay, S. D. Bartlett, L. T. Stephenson, and B. C. Sanders, "Quantum walks in higher dimensions," J. Phys. A 35, 2745-2753 (2002).
[CrossRef]

Meekhof, D. M.

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

Milburn, G. J.

B. C. Travaglione and G. J. Milburn, "Implementing the quantum random walk," Phys. Rev. A 65, 032310 (2002).
[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
[CrossRef] [PubMed]

Mitchell, J. R.

P. G. Kwiat, J. R. Mitchell, P. D. D. Schwindt, and A. G. White, "Grover's search algorithm: an optical approach," J. Mod. Opt. 47, 257-266 (2000).
[CrossRef]

Molina-Terriza, G.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Monroe, C.

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

Mosca, M.

J. A. Jones and M. Mosca, "Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer," J. Chem. Phys. 109, 1648-1653 (1998).
[CrossRef]

J. A. Jones, M. Mosca, and R. H. Hansen, "Implementation of a quantum search algorithm on a quantum computer," Nature 393, 344-346 (1998).
[CrossRef]

O'Brien, J. L.

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

Pittman, T. B.

T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, "Experimental controlled-NOT logic gate for single photons in the coincidence basis," Phys. Rev. A 68, 032316 (2003).
[CrossRef]

Poppe, A.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Pryde, G. J.

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

Ralph, T. C.

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

Resch, K.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Riebe, M.

S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
[CrossRef] [PubMed]

Sanders, B. C.

T. D. Mackay, S. D. Bartlett, L. T. Stephenson, and B. C. Sanders, "Quantum walks in higher dimensions," J. Phys. A 35, 2745-2753 (2002).
[CrossRef]

Schmidt-Kaler, F.

S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
[CrossRef] [PubMed]

Schwindt, P. D. D.

P. G. Kwiat, J. R. Mitchell, P. D. D. Schwindt, and A. G. White, "Grover's search algorithm: an optical approach," J. Mod. Opt. 47, 257-266 (2000).
[CrossRef]

Sciarrino, F.

F. De Martini, V. Buzek, F. Sciarrino, and C. Sias, "Experimental realization of the quantum universal NOT gate," Nature 419, 815-818 (2002).
[CrossRef] [PubMed]

Shor, P. W.

P. W. Shor, "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer," SIAM J. Comput. 26, 1484-1509 (1997).
[CrossRef]

Sias, C.

F. De Martini, V. Buzek, F. Sciarrino, and C. Sias, "Experimental realization of the quantum universal NOT gate," Nature 419, 815-818 (2002).
[CrossRef] [PubMed]

Steffen, M.

L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, "Experimental realization of an order-finding algorithm with an NMR quantum computer," Phys. Rev. Lett. 85, 5452-5455 (2000).
[CrossRef]

Stephenson, L. T.

T. D. Mackay, S. D. Bartlett, L. T. Stephenson, and B. C. Sanders, "Quantum walks in higher dimensions," J. Phys. A 35, 2745-2753 (2002).
[CrossRef]

Taraba, M.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Travaglione , B. C.

B. C. Travaglione and G. J. Milburn, "Implementing the quantum random walk," Phys. Rev. A 65, 032310 (2002).
[CrossRef]

Ursin, R.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Vandersypen, L. M.

L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, "Experimental realization of an order-finding algorithm with an NMR quantum computer," Phys. Rev. Lett. 85, 5452-5455 (2000).
[CrossRef]

Vandersypen, L. M. K.

I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd, "Experimental realization of a quantum algorithm," Nature 393, 143-146 (1998).
[CrossRef]

Walther, P.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

White, A. G.

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

P. G. Kwiat, J. R. Mitchell, P. D. D. Schwindt, and A. G. White, "Grover's search algorithm: an optical approach," J. Mod. Opt. 47, 257-266 (2000).
[CrossRef]

Wineland, D. J.

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

Wojcik, A.

M. Bednarska, A. Grudkà, P. Kurzynski, T. Luczak, and A. Wojcik, "Quantum walks on cycles," Phys. Lett. A 317, 21-25 (2003).
[CrossRef]

Yannoni, C. S.

L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, "Experimental realization of an order-finding algorithm with an NMR quantum computer," Phys. Rev. Lett. 85, 5452-5455 (2000).
[CrossRef]

Zagury, N.

Y. Aharonov, L. Davidovich, and N. Zagury, "Quantum random walks," Phys. Rev. A 48, 1687-1690 (1993).
[CrossRef] [PubMed]

Zeilinger, A.

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

Zhou, X. L.

I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd, "Experimental realization of a quantum algorithm," Nature 393, 143-146 (1998).
[CrossRef]

Chem. Phys. Lett.

N. Linden, H. Barjat, and R. Freeman, "An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer," Chem. Phys. Lett. 296, 61-67 (1998).
[CrossRef]

J. Chem. Phys.

J. A. Jones and M. Mosca, "Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer," J. Chem. Phys. 109, 1648-1653 (1998).
[CrossRef]

J. Mod. Opt.

P. G. Kwiat, J. R. Mitchell, P. D. D. Schwindt, and A. G. White, "Grover's search algorithm: an optical approach," J. Mod. Opt. 47, 257-266 (2000).
[CrossRef]

J. Phys. A

T. D. Mackay, S. D. Bartlett, L. T. Stephenson, and B. C. Sanders, "Quantum walks in higher dimensions," J. Phys. A 35, 2745-2753 (2002).
[CrossRef]

Nature

F. Galton, "Typical laws of heredity," Nature 15, 492-495 , 512-514, 532-533 (1877).
[CrossRef]

C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature 404, 247-255 (2000).
[CrossRef] [PubMed]

J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, "Demonstration of an all-optical quantum controlled-NOT gate," Nature 426, 264-267 (2003).
[CrossRef] [PubMed]

S. Gulde, M. Riebe, G. P. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, "Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer," Nature 421, 48-50 (2003).
[CrossRef] [PubMed]

I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd, "Experimental realization of a quantum algorithm," Nature 393, 143-146 (1998).
[CrossRef]

E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," Nature 409, 46-52 (2001).
[CrossRef] [PubMed]

F. De Martini, V. Buzek, F. Sciarrino, and C. Sias, "Experimental realization of the quantum universal NOT gate," Nature 419, 815-818 (2002).
[CrossRef] [PubMed]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003).
[CrossRef] [PubMed]

A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, "Stimulated emission of polarization-entangled photons," Nature 412, 887-890 (2001).
[CrossRef] [PubMed]

J. A. Jones, M. Mosca, and R. H. Hansen, "Implementation of a quantum search algorithm on a quantum computer," Nature 393, 344-346 (1998).
[CrossRef]

Phys. Lett. A

M. Bednarska, A. Grudkà, P. Kurzynski, T. Luczak, and A. Wojcik, "Quantum walks on cycles," Phys. Lett. A 317, 21-25 (2003).
[CrossRef]

Phys. Rev. A

T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, "Experimental controlled-NOT logic gate for single photons in the coincidence basis," Phys. Rev. A 68, 032316 (2003).
[CrossRef]

B. C. Travaglione and G. J. Milburn, "Implementing the quantum random walk," Phys. Rev. A 65, 032310 (2002).
[CrossRef]

Y. Aharonov, L. Davidovich, and N. Zagury, "Quantum random walks," Phys. Rev. A 48, 1687-1690 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett.

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

I. L. Chuang, N. Gershenfeld, and M. Kubinec, "Experimen-tal implementation of fast quantum searching," Phys. Rev. Lett. 80, 3408-3411 (1998).
[CrossRef]

L. M. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, "Experimental realization of an order-finding algorithm with an NMR quantum computer," Phys. Rev. Lett. 85, 5452-5455 (2000).
[CrossRef]

L. K. Grover, "Quantum mechanics helps in searching for a needle in a haystack," Phys. Rev. Lett. 79, 325-328 (1997).
[CrossRef]

Proc. R. Soc. London

D. Deutsch and R. Jozsa, "Rapid solution of problems by quantum computation," Proc. R. Soc. London 439, 553-558 (1992).
[CrossRef]

Science

D. P. Divincenzo, "Quantum computation," Science 270, 255-261 (1995).
[CrossRef]

M. Aspelmeyer, H. R. Bohm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, "Long-distance free-space distribution of quantum entanglement," Science 301, 621-623 (2003).
[CrossRef] [PubMed]

SIAM J. Comput.

P. W. Shor, "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer," SIAM J. Comput. 26, 1484-1509 (1997).
[CrossRef]

Other

W. Dur, R. Raussendorf, V. M. Kendon, and H.-J. Briegel, "Quantum random walks in optical lattices," e-print quant-ph/0207137, http://www.arxiv.org/abs/quant-ph?0207137.

D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, "Quantum walks on graphs," e-print quant-ph/0012090, http://www.arxiv.org/abs/quant-ph?0012090.

A. M. Childs, R. Cleve, E. Deotto, E. Fahri, S. Gutmann, and D. A. Spielman, "Exponential algorithmic speedup by quantum walk," e-print quant-ph/0209131, http://www.arxiv.org/abs/quant-ph?0209131.

J. Preskill, "Quantum information and computation," Caltech Lecture Notes, http://www.theory.caltech.edu/people/preskill/ph229/lecture, Sec. 6.

M. L. Stohler, "Quantum game theory," Ph.D. thesis (Purdue University, West Lafayette, Ind.), manuscript available from the author.

B. C. Sanders, S. D. Bartlett, B. Tregenna, and P. L. Knight, "Quantum quincunx in cavity quantum electrodynamics," e-print quant-ph/0207028, http://www.arxiv.org/abs/quant-ph?0207028.

A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman, "Exponential algorithmic speedup by quantum walk," e-print quant-ph/0209131, http://www.arxiv.org/abs/quant-ph?0209131.

A. M. Childs, E. Farhi, and S. Gutmann, "An example of the difference between quantum and classical random walks," e-print quant-ph/0103020, http://www.arxiv.org/abs/quant-ph?0103020.

A. Nayak and A. Vishwanath, "Quantum walk on the line," e-print quant-ph/0010117, http://www.arxiv.org/abs/quant-ph?0010117.

D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, "Quantum walks on graphs," e-print quant-ph/0012090, http://www.arxiv.org/abs/quant-ph?0012090.

Z. Zhao, J. Du, H. Li, T. Yang, Z.-B. Chen, and J.-W. Pan, "Implement quantum random walks with linear optics elements," e-print quant-ph/0212149, http://www.arxiv.org/abs/quant-ph?0212149.

W. Dur, R. Raussendorf, V. M. Kendon, and H.-J. Briegel, "Quantum random walks in optical lattices," e-print quant-ph/0207137, http://www.arxiv.org/abs/quant-ph?0207137.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Idealized random walk by use of quantum objects. Each node of the quincunx implements a Hadamard transformation, as described in Eq. (2), along with a translation.

Fig. 2
Fig. 2

Idealized implementation of a quantum quincunx by use of optical elements.

Fig. 3
Fig. 3

Actual realization of the quantum quincunx used in the present experiment.

Fig. 4
Fig. 4

Photograph of the apparatus in operation.

Fig. 5
Fig. 5

Comparison of theory and experiment for the five-layer quantum quincunx. The results are shown for initial polarization angles θ=π/4 and θ=π/2. The phase adjustments were made for θ=π/4, and data were taken in addition at θ=3π/4, π/8, and 0. The level of agreement between and experiment for these angles was similar to that shown in θ=π/2.

Tables (5)

Tables Icon

Table 1 Normalized Theoretical Detector Voltages for Each Polarization Angle

Tables Icon

Table 2 Normalized Observed Detector Voltages for Each Polarization Angle: Trial 1

Tables Icon

Table 3 Normalized Observed Detector Voltages for Each Polarization Angle: Trial 2

Tables Icon

Table 4 Normalized Observed Detector Voltages for Each Polarization Angle: Trial 3

Tables Icon

Table 5 Normalized Observed Detector Voltages for Each Polarization Angle: Trial 4

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

C=n,t|n, t, xn, t, x|+n[|n, v, yn, h, y|+|n, h, yn, v, y|].
H=n,t[|n, tH|xn, t, x|+|n, tH|yn, t, y|],
H=H-1=12 111-1.
T=n,p|n-1, v, pn, v, p|+|n+1, h, pn, h, p|.
|output=[THC]m|0, v, p.

Metrics