Abstract

The concept of nonseparability between spin and orbital degrees of freedom of laser modes is applied in the implementation of the quantum prisoners dilemma. The quantum version of the game brings novel features with a richer universe of strategies and is one of the basic examples to illustrate the concepts of game theory. Exploiting the classical paraxial spin–orbit modes, we implemented the most important strategies that can be achieved in the quantum version of the game.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. A. Meyer, “Quantum strategies,” Phys. Rev. Lett. 82, 1052–1055 (1999).
    [CrossRef]
  2. H. Guo, J. Zhang, and G. J. Koehler, “A survey of quantum games,” Decis. Support Syst. 46, 318–332 (2008).
  3. D. Challet and Y.-C. Zhang, “Emergence of cooperation and organization in an evolutionary game,” Physica A 246, 407–418 (1997).
    [CrossRef]
  4. J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, and R. Han, “Experimental realization of quantum games on a quantum computer,” Phys. Rev. Lett. 88, 137902 (2002).
    [CrossRef]
  5. C. Schmid, A. P. Flitney, W. Wieczorek, N. Kiesel, H. Weinfurter, and L. C. L. Hollenberg, “Experimental implementation of a four-player quantum game,” New J. Phys. 12, 063031 (2010).
    [CrossRef]
  6. W. H. Press and F. J. Dyson, “Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent,” Proc. Natl. Acad. Sci. USA 109, 10409–10413 (2012).
  7. N. Brunner and N. Linden, “Connection between Bell nonlocality and Bayesian game theory,” Nat. Commun. 4, 2057 (2013).
  8. T. Cheon and A. Iqbal, “Nash equilibria and Bell inequalities,” J. Phys. Soc. Jpn. 77, 024801 (2008).
    [CrossRef]
  9. R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
    [CrossRef]
  10. C. E. R. Souza, J. A. O. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit laser moders,” Phys. Rev. Lett. 99, 160401 (2007).
    [CrossRef]
  11. C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 032345 (2008).
    [CrossRef]
  12. L. Chen and W. She, “Single-photon spin-orbit entanglement violating a Bell-like inequality,” J. Opt. Soc. Am. B 27, A7–A10 (2010).
    [CrossRef]
  13. C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin–orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
    [CrossRef]
  14. E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
    [CrossRef]
  15. K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
    [CrossRef]
  16. E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
    [CrossRef]
  17. B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104, 023901 (2010).
    [CrossRef]
  18. A. Yariv, Quantum Electronics (Wiley, 1989).
  19. M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999).
    [CrossRef]
  20. W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
    [CrossRef]
  21. A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33, 13–15 (2008).
    [CrossRef]
  22. V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun. 283, 861–864 (2010).
    [CrossRef]
  23. F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
    [CrossRef]
  24. J. Eisert, M. Wilkens, and M. Lewenstein, “Quantum games and quantum strategies,” Phys. Rev. Lett. 83, 3077–3080 (1999).
    [CrossRef]
  25. M. Paternostro, M. S. Tame, and M. S. Kim, “Hybrid cluster state proposal for a quantum game,” New J. Phys. 7, 1–9 (2005).
    [CrossRef]
  26. R. Prevedel, A. Stefanov, P. Walther, and A. Zeilinger, “Experimental realization of a quantum game on a one-way quantum computer,” New J. Phys. 9, 1–11 (2007).
    [CrossRef]
  27. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
    [CrossRef]
  28. H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
    [CrossRef]

2013 (2)

N. Brunner and N. Linden, “Connection between Bell nonlocality and Bayesian game theory,” Nat. Commun. 4, 2057 (2013).

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

2012 (2)

W. H. Press and F. J. Dyson, “Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent,” Proc. Natl. Acad. Sci. USA 109, 10409–10413 (2012).

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[CrossRef]

2010 (6)

L. Chen and W. She, “Single-photon spin-orbit entanglement violating a Bell-like inequality,” J. Opt. Soc. Am. B 27, A7–A10 (2010).
[CrossRef]

V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun. 283, 861–864 (2010).
[CrossRef]

C. Schmid, A. P. Flitney, W. Wieczorek, N. Kiesel, H. Weinfurter, and L. C. L. Hollenberg, “Experimental implementation of a four-player quantum game,” New J. Phys. 12, 063031 (2010).
[CrossRef]

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin–orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[CrossRef]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

2009 (1)

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef]

2008 (4)

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 032345 (2008).
[CrossRef]

T. Cheon and A. Iqbal, “Nash equilibria and Bell inequalities,” J. Phys. Soc. Jpn. 77, 024801 (2008).
[CrossRef]

H. Guo, J. Zhang, and G. J. Koehler, “A survey of quantum games,” Decis. Support Syst. 46, 318–332 (2008).

A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33, 13–15 (2008).
[CrossRef]

2007 (2)

R. Prevedel, A. Stefanov, P. Walther, and A. Zeilinger, “Experimental realization of a quantum game on a one-way quantum computer,” New J. Phys. 9, 1–11 (2007).
[CrossRef]

C. E. R. Souza, J. A. O. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit laser moders,” Phys. Rev. Lett. 99, 160401 (2007).
[CrossRef]

2005 (1)

M. Paternostro, M. S. Tame, and M. S. Kim, “Hybrid cluster state proposal for a quantum game,” New J. Phys. 7, 1–9 (2005).
[CrossRef]

2003 (1)

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[CrossRef]

2002 (1)

J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, and R. Han, “Experimental realization of quantum games on a quantum computer,” Phys. Rev. Lett. 88, 137902 (2002).
[CrossRef]

1999 (3)

D. A. Meyer, “Quantum strategies,” Phys. Rev. Lett. 82, 1052–1055 (1999).
[CrossRef]

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999).
[CrossRef]

J. Eisert, M. Wilkens, and M. Lewenstein, “Quantum games and quantum strategies,” Phys. Rev. Lett. 83, 3077–3080 (1999).
[CrossRef]

1998 (2)

R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[CrossRef]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

1997 (1)

D. Challet and Y.-C. Zhang, “Emergence of cooperation and organization in an evolutionary game,” Physica A 246, 407–418 (1997).
[CrossRef]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Abouraddy, A. F.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Aolita, L.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 032345 (2008).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Borges, C. V. S.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin–orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[CrossRef]

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 032345 (2008).
[CrossRef]

Borghi, R.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Brunner, N.

N. Brunner and N. Linden, “Connection between Bell nonlocality and Bayesian game theory,” Nat. Commun. 4, 2057 (2013).

Cardano, F.

Challet, D.

D. Challet and Y.-C. Zhang, “Emergence of cooperation and organization in an evolutionary game,” Physica A 246, 407–418 (1997).
[CrossRef]

Chen, L.

Chen, L. X.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

Cheon, T.

T. Cheon and A. Iqbal, “Nash equilibria and Bell inequalities,” J. Phys. Soc. Jpn. 77, 024801 (2008).
[CrossRef]

Courtial, J.

de Lisio, C.

De Martini, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef]

Di Giuseppe, G.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

Du, J.

J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, and R. Han, “Experimental realization of quantum games on a quantum computer,” Phys. Rev. Lett. 88, 137902 (2002).
[CrossRef]

Dyson, F. J.

W. H. Press and F. J. Dyson, “Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent,” Proc. Natl. Acad. Sci. USA 109, 10409–10413 (2012).

Eisert, J.

J. Eisert, M. Wilkens, and M. Lewenstein, “Quantum games and quantum strategies,” Phys. Rev. Lett. 83, 3077–3080 (1999).
[CrossRef]

Flitney, A. P.

C. Schmid, A. P. Flitney, W. Wieczorek, N. Kiesel, H. Weinfurter, and L. C. L. Hollenberg, “Experimental implementation of a four-player quantum game,” New J. Phys. 12, 063031 (2010).
[CrossRef]

Franke-Arnold, S.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

Gaeta, A. L.

Gori, F.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Grow, T. D.

Guo, H.

H. Guo, J. Zhang, and G. J. Koehler, “A survey of quantum games,” Decis. Support Syst. 46, 318–332 (2008).

Han, R.

J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, and R. Han, “Experimental realization of quantum games on a quantum computer,” Phys. Rev. Lett. 88, 137902 (2002).
[CrossRef]

Hollenberg, L. C. L.

C. Schmid, A. P. Flitney, W. Wieczorek, N. Kiesel, H. Weinfurter, and L. C. L. Hollenberg, “Experimental implementation of a four-player quantum game,” New J. Phys. 12, 063031 (2010).
[CrossRef]

Hor-Meyll, M.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin–orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[CrossRef]

Huguenin, J. A. O.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin–orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[CrossRef]

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 032345 (2008).
[CrossRef]

C. E. R. Souza, J. A. O. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit laser moders,” Phys. Rev. Lett. 99, 160401 (2007).
[CrossRef]

Inavalli, V. V. G. K.

V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun. 283, 861–864 (2010).
[CrossRef]

Iqbal, A.

T. Cheon and A. Iqbal, “Nash equilibria and Bell inequalities,” J. Phys. Soc. Jpn. 77, 024801 (2008).
[CrossRef]

Ishaaya, A. A.

Kagalwala, K. H.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

Karimi, E.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[CrossRef]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef]

Khoury, A. Z.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin–orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[CrossRef]

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 032345 (2008).
[CrossRef]

C. E. R. Souza, J. A. O. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit laser moders,” Phys. Rev. Lett. 99, 160401 (2007).
[CrossRef]

Kiesel, N.

C. Schmid, A. P. Flitney, W. Wieczorek, N. Kiesel, H. Weinfurter, and L. C. L. Hollenberg, “Experimental implementation of a four-player quantum game,” New J. Phys. 12, 063031 (2010).
[CrossRef]

Kim, M. S.

M. Paternostro, M. S. Tame, and M. S. Kim, “Hybrid cluster state proposal for a quantum game,” New J. Phys. 7, 1–9 (2005).
[CrossRef]

Koehler, G. J.

H. Guo, J. Zhang, and G. J. Koehler, “A survey of quantum games,” Decis. Support Syst. 46, 318–332 (2008).

Leach, J.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

Lewenstein, M.

J. Eisert, M. Wilkens, and M. Lewenstein, “Quantum games and quantum strategies,” Phys. Rev. Lett. 83, 3077–3080 (1999).
[CrossRef]

Li, H.

J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, and R. Han, “Experimental realization of quantum games on a quantum computer,” Phys. Rev. Lett. 88, 137902 (2002).
[CrossRef]

Linden, N.

N. Brunner and N. Linden, “Connection between Bell nonlocality and Bayesian game theory,” Nat. Commun. 4, 2057 (2013).

Marrucci, L.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[CrossRef]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef]

Meyer, D. A.

D. A. Meyer, “Quantum strategies,” Phys. Rev. Lett. 82, 1052–1055 (1999).
[CrossRef]

Milman, P.

C. E. R. Souza, J. A. O. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit laser moders,” Phys. Rev. Lett. 99, 160401 (2007).
[CrossRef]

Mukunda, N.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Nagali, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef]

Okamoto, M.

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[CrossRef]

Padgett, M. J.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999).
[CrossRef]

Paternostro, M.

M. Paternostro, M. S. Tame, and M. S. Kim, “Hybrid cluster state proposal for a quantum game,” New J. Phys. 7, 1–9 (2005).
[CrossRef]

Piccirillo, B.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef]

Press, W. H.

W. H. Press and F. J. Dyson, “Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent,” Proc. Natl. Acad. Sci. USA 109, 10409–10413 (2012).

Prevedel, R.

R. Prevedel, A. Stefanov, P. Walther, and A. Zeilinger, “Experimental realization of a quantum game on a one-way quantum computer,” New J. Phys. 9, 1–11 (2007).
[CrossRef]

Saleh, B. E. A.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

Santamato, E.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[CrossRef]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef]

Santarsiero, M.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Sasada, H.

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[CrossRef]

Schmid, C.

C. Schmid, A. P. Flitney, W. Wieczorek, N. Kiesel, H. Weinfurter, and L. C. L. Hollenberg, “Experimental implementation of a four-player quantum game,” New J. Phys. 12, 063031 (2010).
[CrossRef]

Sciarrino, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef]

She, W.

She, W. L.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

Shi, M.

J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, and R. Han, “Experimental realization of quantum games on a quantum computer,” Phys. Rev. Lett. 88, 137902 (2002).
[CrossRef]

Simon, B. N.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Simon, R.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Simon, S.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

Slussarenko, S.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[CrossRef]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

Souza, C. E. R.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 032345 (2008).
[CrossRef]

C. E. R. Souza, J. A. O. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit laser moders,” Phys. Rev. Lett. 99, 160401 (2007).
[CrossRef]

Spreeuw, R. J. C.

R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[CrossRef]

Stefanov, A.

R. Prevedel, A. Stefanov, P. Walther, and A. Zeilinger, “Experimental realization of a quantum game on a one-way quantum computer,” New J. Phys. 9, 1–11 (2007).
[CrossRef]

Tame, M. S.

M. Paternostro, M. S. Tame, and M. S. Kim, “Hybrid cluster state proposal for a quantum game,” New J. Phys. 7, 1–9 (2005).
[CrossRef]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Viswanathan, N. K.

V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun. 283, 861–864 (2010).
[CrossRef]

Vuong, L. T.

Walborn, S. P.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 032345 (2008).
[CrossRef]

Walther, P.

R. Prevedel, A. Stefanov, P. Walther, and A. Zeilinger, “Experimental realization of a quantum game on a one-way quantum computer,” New J. Phys. 9, 1–11 (2007).
[CrossRef]

Weinfurter, H.

C. Schmid, A. P. Flitney, W. Wieczorek, N. Kiesel, H. Weinfurter, and L. C. L. Hollenberg, “Experimental implementation of a four-player quantum game,” New J. Phys. 12, 063031 (2010).
[CrossRef]

Wieczorek, W.

C. Schmid, A. P. Flitney, W. Wieczorek, N. Kiesel, H. Weinfurter, and L. C. L. Hollenberg, “Experimental implementation of a four-player quantum game,” New J. Phys. 12, 063031 (2010).
[CrossRef]

Wilkens, M.

J. Eisert, M. Wilkens, and M. Lewenstein, “Quantum games and quantum strategies,” Phys. Rev. Lett. 83, 3077–3080 (1999).
[CrossRef]

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Wootters, W. K.

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

Wu, J.

J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, and R. Han, “Experimental realization of quantum games on a quantum computer,” Phys. Rev. Lett. 88, 137902 (2002).
[CrossRef]

Xu, X.

J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, and R. Han, “Experimental realization of quantum games on a quantum computer,” Phys. Rev. Lett. 88, 137902 (2002).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, 1989).

Zeilinger, A.

R. Prevedel, A. Stefanov, P. Walther, and A. Zeilinger, “Experimental realization of a quantum game on a one-way quantum computer,” New J. Phys. 9, 1–11 (2007).
[CrossRef]

Zhang, J.

H. Guo, J. Zhang, and G. J. Koehler, “A survey of quantum games,” Decis. Support Syst. 46, 318–332 (2008).

Zhang, Y.-C.

D. Challet and Y.-C. Zhang, “Emergence of cooperation and organization in an evolutionary game,” Physica A 246, 407–418 (1997).
[CrossRef]

Zhou, X.

J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, and R. Han, “Experimental realization of quantum games on a quantum computer,” Phys. Rev. Lett. 88, 137902 (2002).
[CrossRef]

Appl. Opt. (1)

Decis. Support Syst. (1)

H. Guo, J. Zhang, and G. J. Koehler, “A survey of quantum games,” Decis. Support Syst. 46, 318–332 (2008).

Found. Phys. (1)

R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Soc. Jpn. (1)

T. Cheon and A. Iqbal, “Nash equilibria and Bell inequalities,” J. Phys. Soc. Jpn. 77, 024801 (2008).
[CrossRef]

Nat. Commun. (1)

N. Brunner and N. Linden, “Connection between Bell nonlocality and Bayesian game theory,” Nat. Commun. 4, 2057 (2013).

Nat. Photonics (1)

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7, 72–78 (2013).
[CrossRef]

New J. Phys. (3)

C. Schmid, A. P. Flitney, W. Wieczorek, N. Kiesel, H. Weinfurter, and L. C. L. Hollenberg, “Experimental implementation of a four-player quantum game,” New J. Phys. 12, 063031 (2010).
[CrossRef]

M. Paternostro, M. S. Tame, and M. S. Kim, “Hybrid cluster state proposal for a quantum game,” New J. Phys. 7, 1–9 (2005).
[CrossRef]

R. Prevedel, A. Stefanov, P. Walther, and A. Zeilinger, “Experimental realization of a quantum game on a one-way quantum computer,” New J. Phys. 9, 1–11 (2007).
[CrossRef]

Opt. Commun. (2)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun. 283, 861–864 (2010).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (4)

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77, 032345 (2008).
[CrossRef]

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[CrossRef]

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin–orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[CrossRef]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. X. Chen, W. L. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[CrossRef]

Phys. Rev. Lett. (7)

C. E. R. Souza, J. A. O. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit laser moders,” Phys. Rev. Lett. 99, 160401 (2007).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103, 013601 (2009).
[CrossRef]

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104, 023901 (2010).
[CrossRef]

D. A. Meyer, “Quantum strategies,” Phys. Rev. Lett. 82, 1052–1055 (1999).
[CrossRef]

J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, and R. Han, “Experimental realization of quantum games on a quantum computer,” Phys. Rev. Lett. 88, 137902 (2002).
[CrossRef]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

J. Eisert, M. Wilkens, and M. Lewenstein, “Quantum games and quantum strategies,” Phys. Rev. Lett. 83, 3077–3080 (1999).
[CrossRef]

Physica A (1)

D. Challet and Y.-C. Zhang, “Emergence of cooperation and organization in an evolutionary game,” Physica A 246, 407–418 (1997).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

W. H. Press and F. J. Dyson, “Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent,” Proc. Natl. Acad. Sci. USA 109, 10409–10413 (2012).

Other (1)

A. Yariv, Quantum Electronics (Wiley, 1989).

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 (3)

Fig. 1.
Fig. 1.

Experimental setup. Step 1: preparation of the initial state. Step 2: strategies of Alice and Bob. Step 3: disentanglement. Step 4: measurement. Below: corresponding logical circuit.

Fig. 2.
Fig. 2.

(a) Coefficients table of the final mode in the computational basis. (b) Images of the corresponding output ports.

Fig. 3.
Fig. 3.

Alice’s payoff as a function of the strategy parameters (θA,ϕA) and (θB,ϕB). The dots correspond to the experimental values obtained with the intensity measurements.

Tables (1)

Tables Icon

Table 1. Penalty Reduction Table

Equations (10)

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

Ψ(r)=αψh(r)e^H+βψv(r)e^H+γψh(r)e^V+δψv(r)e^V,
Ψ0(r)=ψh(r)e^H+iψv(r)e^V2.
$j=m,n=C,Dp(m,n)Rj(m,n),
J=[100i01i00i10i001],
MZ(ϕ)=[10000100000eiϕ00eiϕ0],
T(θ,ϕ)=[cosϕ2+isinϕ2cos2θisinϕ2sin2θisinϕ2sin2θcosϕ2isinϕ2cos2θ].
Ψ1(r)=[T(θA,ϕA)T(θB,ϕB)]Ψ0(r).
J=MZ(0)[T(45°,π/2)I]MZ(π/2),
Ψ2(r)=JΨ1(r)=m,ncmnψm(r)e^n,
p(m,n)=|cmn|2=|d2rψm*(r)[e^n*·Ψ2(r)]|2,

Metrics