Quantum entanglement distillation with metamaterials.

We propose a scheme for the distillation of partially entangled two-photon Bell and three-photon W states using metamaterials. The distillation of partially entangled Bell states is achieved by using two metamaterials with polarization dependence, one of which is rotated by π/2 around the direction of propagation of the photons. On the other hand, the distillation of three-photon W states is achieved by using one polarization dependent metamaterial and two polarization independent metamaterials. Upon transmission of the photons of the partially entangled states through the metamaterials the entanglement of the states increases and they become distilled. This work opens up new directions in quantum optical state engineering by showing how metamaterials can be used to carry out a quantum information processing task.

[1]  Patrick Mounaix,et al.  Tunable terahertz metamaterials with negative permeability , 2009 .

[2]  Iam-Choon Khoo,et al.  Liquid crystal clad near-infrared metamaterials with tunable negative-zero-positive refractive indices. , 2007, Optics express.

[3]  David R. Smith,et al.  Electromagnetic parameter retrieval from inhomogeneous metamaterials. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Surface plasmon driven electric and magnetic resonators for metamaterials , 2011, 1104.1956.

[5]  E. Ulin-Avila,et al.  Three-dimensional optical metamaterial with a negative refractive index , 2008, Nature.

[6]  M. A. Osipov,et al.  Tunability of wire-grid metamaterial immersed into nematic liquid crystal , 2007, 0708.4286.

[7]  A. Zeilinger,et al.  Local Conversion of Greenberger-Horne-Zeilinger States to Approximate W States , 2005 .

[8]  M. Ligare.  Propagation of quantized fields through negative-index media , 2011 .

[9]  ON NEGATIVE INDEX METAMATERIAL SPACERS AND THEIR UNUSUAL OPTICAL PROPERTIES , 2012, 1212.6681.

[10]  Chuan Wang,et al.  Efficient W-state entanglement concentration using quantum-dot and optical microcavities , 2012, 1206.5664.

[11]  Ekmel Ozbay,et al.  Compact size highly directive antennas based on the SRR metamaterial medium , 2005 .

[12]  P. Kužel,et al.  Transition between metamaterial and photonic-crystal behavior in arrays of dielectric rods. , 2014, Optics express.

[13]  Bin Gu.  Single-photon-assisted entanglement concentration of partially entangled multiphoton W states with linear optics , 2012 .

[14]  H. Mosallaei,et al.  Tunable negative refractive index metamaterial phase shifter , 2007, 2007 IEEE Antennas and Propagation Society International Symposium.

[15]  M Paternostro,et al.  Single-photon excitation of surface plasmon polaritons. , 2008, Physical review letters.

[16]  Steven A. Cummer,et al.  Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings , 2008 .

[17]  Durdu Ö. Güney,et al.  Intra-connected three-dimensionally isotropic bulk negative index photonic metamaterial. , 2010, Optics express.

[18]  David R. Smith,et al.  Metamaterial Electromagnetic Cloak at Microwave Frequencies , 2006, Science.

[19]  J. Pendry,et al.  Negative refraction makes a perfect lens , 2000, Physical review letters.

[20]  J. Cirac,et al.  Theory of plasmon-assisted transmission of entangled photons. , 2003, Physical review letters.

[21]  Dual-band, double-negative, polarization-independent metamaterial for the visible spectrum , 2012, 1209.0792.

[22]  M. Koashi,et al.  Experimental extraction of an entangled photon pair from two identically decohered pairs , 2003, Nature.

[23]  Fernando L. Teixeira,et al.  Electrically small, complementary electric-field-coupled resonator antennas , 2013 .

[24]  D. Smith,et al.  Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients , 2001, physics/0111203.

[25]  M. Kim,et al.  Quantum theory of surface-plasmon polariton scattering , 2010, 1002.1051.

[26]  Masato Koashi,et al.  An optical fusion gate for W-states , 2011, 1103.2195.

[27]  Lan Zhou,et al.  Efficient entanglement concentration for arbitrary single-photon multimode W state , 2012, 1210.6178.

[28]  Maria Kafesaki,et al.  Negative refractive index response of weakly and strongly coupled optical metamaterials , 2009, 0907.1119.

[29]  Stefan A. Maier,et al.  Quantum Plasmonics , 2016, Proceedings of the IEEE.

[30]  Yuri Kivshar,et al.  Structural tunability in metamaterials , 2009, 0907.2303.

[31]  D. Meyer,et al.  Global entanglement in multiparticle systems , 2001, quant-ph/0108104.

[32]  O. Sigmund,et al.  A Review of the Scattering-Parameter Extraction Method with Clarification of Ambiguity Issues in Relation to Metamaterial Homogenization , 2012, IEEE Antennas and Propagation Magazine.

[33]  Creation of entanglement and implementation of quantum logic gate operations using a three-dimensional photonic crystal single-mode cavity , 2006, quant-ph/0603087.

[34]  Masato Koashi,et al.  Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace , 2008, 0806.2896.

[35]  Jelena Vucković,et al.  Design of photonic crystal microcavities for cavity QED. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  M. Wegener,et al.  Negative-index metamaterial at 780 nm wavelength. , 2006, Optics letters.

[37]  R. J. Bell,et al.  Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared. , 1983, Applied optics.

[38]  Masato Koashi,et al.  Demonstration of local expansion toward large-scale entangled webs. , 2010, Physical review letters.

[39]  Masato Koashi,et al.  Local expansion of photonic W state using a polarization-dependent beamsplitter , 2008, 0810.2850.

[40]  Bin Gu,et al.  Multi-photon Entanglement Concentration Protocol for Partially Entangled W States with Projection Measurement , 2012, International Journal of Theoretical Physics.

[41]  M. Tame,et al.  Long-range surface plasmon polariton excitation at the quantum level , 2009, 0901.3972.

[42]  Xiao Liang,et al.  Electrically tunable negative permeability metamaterials based on nematic liquid crystals , 2007 .

[43]  Stefan Linden,et al.  Bianisotropic Photonic Metamaterials , 2010, IEEE Journal of Selected Topics in Quantum Electronics.

[44]  C. Beenakker,et al.  Scattering theory of plasmon-assisted entanglement transfer and distillation , 2002, quant-ph/0211103.

[45]  Peter W. Milonni,et al.  Field Quantization and Radiative Processes in Dispersive Dielectric Media , 1995 .

[46]  R. Pooser,et al.  Extraordinary optical transmission of multimode quantum correlations via localized surface plasmons. , 2012, Physical review letters.

[47]  Sahin Kaya Ozdemir,et al.  Fusing multiple W states simultaneously with a Fredkin gate , 2014, 1402.3152.

[48]  N. Gisin,et al.  Experimental entanglement distillation and ‘hidden’ non-locality , 2001, Nature.

[49]  G. J. Maclay,et al.  Quantized-field description of light in negative-index media , 2003 .

[50]  D. Meyer,et al.  Negative refraction gives rise to the Klein paradox , 2009, 0907.0265.

[51]  Changtao Wang,et al.  Sub-diffraction-limited interference photolithography with metamaterials. , 2008, Optics express.

[52]  Masato Koashi,et al.  Local transformation of two einstein-podolsky-rosen photon pairs into a three-photon w state. , 2008, Physical review letters.

[53]  S. Linden,et al.  Photonic metamaterials by direct laser writing and silver chemical vapour deposition. , 2008, Nature materials.

[54]  A. Zayats,et al.  Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths. , 2011, Physical review letters.

[55]  Bulk Negative Index Photonic Metamaterials for Direct Laser Writing , 2008, 0807.4560.

[56]  Fuguo Deng,et al.  Single-photon-assisted entanglement concentration of a multiphoton system in a partially entangled W state with weak cross-Kerr nonlinearity , 2012, 1208.0105.

[57]  J. P. Woerdman,et al.  Plasmon-assisted transmission of entangled photons , 2002, Nature.

[58]  Jin Au Kong,et al.  Robust method to retrieve the constitutive effective parameters of metamaterials. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  U. Leonhardt,et al.  Quantum levitation by left-handed metamaterials , 2006, quant-ph/0608115.

[60]  M. Aslam,et al.  Surface plasmon driven scalable low-loss negative-index metamaterial in the visible spectrum , 2011, 1111.3655.

[61]  G. Long,et al.  Entanglement concentration for arbitrary unknown less-entangled three-photon W states with linear optics , 2013 .

[62]  Durdu Ö. Güney,et al.  Connected bulk negative index photonic metamaterials. , 2009, Optics letters.

[63]  S. Maier,et al.  Tunable negative permeability in a quantum plasmonic metamaterial , 2014, 1401.5402.

[64]  Abul K. Azad,et al.  Experimental demonstration of frequency-agile terahertz metamaterials , 2008 .

[65]  E. Knill,et al.  Experimental purification of two-atom entanglement , 2006, Nature.

[66]  D. Genov,et al.  Mimicking celestial mechanics in metamaterials , 2009 .

[67]  Integrated conditional teleportation and readout circuit based on a photonic crystal single chip , 2006, quant-ph/0605067.

[68]  Joshua M. Pearce,et al.  Exchanging Ohmic Losses in Metamaterial Absorbers with Useful Optical Absorption for Photovoltaics , 2014, Scientific Reports.