Hardy’s nonlocality proof is considered as “the best version of Bell’s theorem”. We report an experimental implementation of this by measuring the orbital angular momentum (OAM) of entangled twisted photon pairs. Two advantages arise from using twisted photons. First, the limited OAM spectrum generated by parametric down-conversion provides a natural set of OAM non-maximally entangled states with selective degrees of entanglement. Second, the measurement of any non-trivial superposition of OAM states can be conveniently done with spatial light modulators. We measure states that are defined on asymmetric OAM Bloch spheres and show results which are incompatible with local realism.

© 2012 OSA

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Ann. N. Y. Acad. Sci.

• N. Mermin, “The best version of Bell’s theorem,” Ann. N. Y. Acad. Sci.755, 616–623 (1995). [CrossRef]

Laser Photonics Rev.

• S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev.2, 299–313 (2008). [CrossRef]

Nat. Phys.

• G. Molina-Terriza, J. Torres, and L. Torner, “Twisted photons,” Nat. Phys.3, 305–310 (2007). [CrossRef]
• M. Dennis, R.P. King, B. Jack, K. O’Holleran, and M.J. Padgett, “Isolated optical vortex knots”, Nat. Phys.6, 118–121 (2010). [CrossRef]

Nature

• A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412, 313–316 (2001). [CrossRef]

New J. Phys.

• M. Wiesniak, T. Paterek, and A. Zeilinger, “Entanglement in mutually unbiased bases,” New J. Phys.13, 053047 (2011). [CrossRef]
• A. Yao, “Spectral decomposition of entangled photons with an arbitrary pump,” New J. Phys.13, 053048 (2011). [CrossRef]

Opt. Express

• J. Leach, B. Jack, J. Romero, M. Ritsch-Marte, R. Boyd, A. Jha, S. Barnett, S. Franke-Arnold, and M. J. Padgett, “Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express10, 8287–8293 (2009). [CrossRef]

Opt. Lett.

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

Phys. Lett. A

• M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, “Towards a test of non-locality without ’supplementary assumptions’,” Phys. Lett. A334, 23–29 (2005). [CrossRef]
• J. Torgerson, D. Branning, C. Monken, and L. Mandel, “Experimental demonstration of the violation of local realism without Bell inequalities,” Phys. Lett. A204, 323–328 (1995). [CrossRef]

Phys. Rep.

• M. Genovese, “Research on hidden variable theories: a review of recent progresses,” Phys. Rep.413, 319–396 (2005). [CrossRef]

Phys. Rev.

• A. Einstein, B. Podolsky, and N. Rosen, “Can quantum mechanical description of reality ever be considered complete?” Phys. Rev.47, 777–780 (1935). [CrossRef]

Phys. Rev. A

• T. Jordan, “Testing einstein-podolsky-rosen assumptions without inequalities with two photons or particles with spin 1/2,” Phys. Rev. A50, 62–66 (1994). [CrossRef]
• G. Vallone, I. Gianani, E. Inostroza, C. Saavedra, G. Lima, A. Cabello, and P. Mataloni, “Testing hardys nonlocality proof with genuine energy-time entanglement,” Phys. Rev. A83, 042105 (2011). [CrossRef]
• G. Di Giuseppe, F. De Martini, and D. Boschi, “Experimental test of the violation of local realism in quantum mechanics without Bell inequalities,” Phys. Rev. A56, 176–181 (1997). [CrossRef]
• B. Jack, A. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. Ireland, S. Barnett, and M. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A81, 43844 (2010). [CrossRef]
• J. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A68, 050301 (2003). [CrossRef]
• J. Romero, D. Giovannini, S. Franke-Anold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A86, 012334 (2012). [CrossRef]

Phys. Rev. Lett.

• D. Boschi, S. Branca, F. De Martini, and L. Hardy, “Ladder proof of nonlocality without inequalities: theoretical and experimental results,” Phys. Rev. Lett.79, 2755–2758 (1997). [CrossRef]
• L. Hardy, “Nonlocality for two particles without inequalities for almost all entangled states,” Phys. Rev. Lett.71, 1665–1668 (1993). [CrossRef]
• S. Goldstein, “Nonlocality without inequalities for almost all entangled states for two particles,” Phys. Rev. Lett.72, 1951–1951 (1994). [CrossRef]
• Y. Shih and C. Alley, “New type of eisntein-podolsky-rosen bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett.61, 2921–2924 (1988). [CrossRef]

Rev. Mod. Phys.

• J. Bell, “On the problem of hidden variables in quantum mechanics,” Rev. Mod. Phys.38, 447–452 (1966). [CrossRef]

Science

• J. Leach, B. Jack, J. Romero, A. Jha, A. Yao, S. Franke-Arnold, D. Ireland, R. Boyd, S. Barnett, and M. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science329, 662 (2010). [CrossRef]

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