Experimental violation of a Bell inequality with two different degrees of freedom of entangled particle pairs

We demonstrate hybrid entanglement of photon pairs via the experimental violation of a Bell inequality with two different degrees of freedom (DOF), namely, the path (linear momentum) of one photon and the polarization of the other photon. Hybrid entangled photon pairs are created by spontaneous parametric down conversion and coherent polarization to path conversion for one photon. For that photon, path superposition is analyzed, and polarization superposition for its twin photon. The correlations between these two measurements give an $S$ parameter of $S=2.653\ifmmode\pm\else\textpm\fi{}0.027$ in a Clauser-Horne-Shimony-Holt inequality and thus violate local realism for two different DOF by more than 24 standard deviations. This experimentally supports the idea that entanglement is a fundamental concept which is indifferent to the specific physical realization of Hilbert space.

[1]  R. Loidl,et al.  Violation of a Bell-like inequality in single-neutron interferometry , 2003, Nature.

[2]  M. Żukowski,et al.  Bell's theorem: Proposition of realizable experiment using linear momenta , 1988 .

[3]  Christian Kurtsiefer,et al.  High efficiency entangled photon pair collection in type II parametric fluorescence , 2001, quant-ph/0101074.

[4]  Nathan K Langford,et al.  Generation of hyperentangled photon pairs. , 2005, Physical review letters.

[5]  Kai Chen,et al.  Experimental realization of one-way quantum computing with two-photon four-qubit cluster states. , 2007, Physical review letters.

[6]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[7]  J. Raimond,et al.  Manipulating quantum entanglement with atoms and photons in a cavity , 2001 .

[8]  H. Weinfurter,et al.  Violation of Bell's Inequality under Strict Einstein Locality Conditions , 1998, quant-ph/9810080.

[9]  P. Grangier,et al.  Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment : A New Violation of Bell's Inequalities , 1982 .

[10]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .

[11]  J. Rarity,et al.  Experimental violation of Bell's inequality based on phase and momentum. , 1990, Physical review letters.

[12]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[13]  M. Żukowski,et al.  Test of the Bell inequality based on phase and linear momentum as well as spin , 1991 .

[14]  Weinfurter,et al.  Experiments towards falsification of noncontextual hidden variable theories , 2000, Physical review letters.

[15]  Matison,et al.  Experimental Test of Local Hidden-Variable Theories , 1972 .

[16]  Shih,et al.  Postselection-free energy-time entanglement. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[17]  J. Cirac,et al.  Long-distance quantum communication with atomic ensembles and linear optics , 2001, Nature.

[18]  G. Vallone,et al.  Realization and characterization of a 2-photon 4-qubit linear cluster state , 2007, 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference.

[19]  Franson,et al.  Bell inequality for position and time. , 1989, Physical review letters.

[20]  A. Shimony,et al.  Two-particle interferometry. , 1989 .

[21]  Shih,et al.  New high-intensity source of polarization-entangled photon pairs. , 1995, Physical review letters.

[22]  Gilles Brassard,et al.  Quantum Cryptography , 2005, Encyclopedia of Cryptography and Security.