We present a scheme for generating entanglement between two spatially separated systems from the spatial entanglement generated by the interference effect during the evolution of a single-particle quantum walk. Any two systems which can interact with the spatial modes entangled during the walk evolution can be entangled using this scheme. A notable feature is the ability to control the quantum walk dynamics and its localization at desired pair lattice sites irrespective of separation distance resulting in a substantial control and improvement in the entanglement output. Implementation schemes to entangle spatially separated atoms using quantum walk on a single atom is also presented.
R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, “Quantum Entanglement,” Reviews of Modern Physics, Vol. 81, No. 2, 2009, pp. 865-942. doi:10.1103/RevModPhys.81.865
T. Brougham, V. Kostak, I. Jex, E. Andersson and T. Kiss, “Entanglement Preparation Using Symmetric Multiports,” The European Physical Journal D, Vol. 61, No. 1, 2011, pp. 231-236. doi:10.1140/epjd/e2010-10337-2.
C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez and P. Zoller, “Creation of Entangled States of Distant Atoms by Interference,” Physical Review A, Vol. 59, No. 2, 1999, pp. 1025-1033. doi:10.1103/PhysRevA.59.1025
M. B. Plenio, S. F. Huelga, A. Beige and P. L. Knight, “Cavity-Loss-Induced Generation of Entangled Atoms,” Physical Review A, Vol. 59, No. 3, 1999, pp. 2468-2475. doi:10.1103/PhysRevA.59.2468
L. Duan, M. D. Lukin, J. I. Cirac and P. Zoller, “Long-Distance Quantum Communication with Atomic Ensembles and Linear Optics,” Nature (London), Vol. 414, 2001, pp. 413-418. doi:10.1038/35106500
S. Bose and D. Home, “Generic Entanglement Generation, Quantum Statistics, and Complementarity,” Physical Review Letters, Vol. 88, 2002, Article ID: 050401. doi:10.1103/PhysRevLett.88.050401
A. K. Ekert, “Quantum Cryptography Based on Bell’s Theorem,” Physical Review Letters, Vol. 67, No. 6, 1991, pp. 661-633. doi:10.1103/PhysRevLett.67.661
C. H. Bennett, “Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels,” Physical Review Letters, Vol. 70, No. 13, 1993, pp. 1895-1899. doi:10.1103/PhysRevLett.70.1895
S. J. van Enk, “Single-Particle Entanglement,” Physical Review A, Vol. 72, No. 6, 2005, Article ID: 064306. doi:10.1103/PhysRevA.72.064306
S. Goyal and C. M. Chandrashekar, “Spatial Entanglement Using a Quantum Walk on a Many-Body System,” Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 23, 2010, Article ID: 235303. doi:10.1088/1751-8113/43/23/235303
D. A. Meyer, “From Quantum Cellular Automata to Quantum Lattice Gases,” Journal of Statistical Physics, Vol. 85, No. 5-6, 1996, pp. 551-574. doi:10.1007/BF02199356
C. M. Chandrashekar, R. Srikanth and R. Laflamme, “Optimizing the Discrete Time Quantum Walk Using a SU(2) Coin,” Physical Review A, Vol. 77, No. 3, 2008, Article ID: 032326. doi:10.1103/PhysRevA.77.032326
J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou and R. Han, “Experimental Implementation of the Quantum Random-Walk Algorithm,” Physical Review A, Vol. 67, No. 4, 2003, Article ID: 042316. doi:10.1103/PhysRevA.67.042316
C. A. Ryan, M. Laforest, J. C. Boileau and R. Laflamme, “Experimental Implementation of a Discrete-Time Quantum Random Walk on an NMR Quantum-Information Processor,” Physical Review A, Vol. 72, No. 6, 2005, Article ID: 062317. doi:10.1103/PhysRevA.72.062317
D. Lu, J. Zhu, P. Zou, X. Peng, Y. Yu, S. Zhang, Q. Chen and J. Du, “Experimental Implementation of a Quantum Random-Walk Search Algorithm Using Strongly Dipolar Coupled Spins,” Physical Review A, Vol. 81, No. 2, 2010, Article ID: 022308. doi:10.1103/PhysRevA.81.022308
D. Bouwmeester, I. Marzoli, G. P. Karman, W. Schleich and J. P. Woerdman, “Optical Galton Board,” Physical Review A, Vol. 61, No. 1, 1999, Article ID: 013410. doi:10.1103/PhysRevA.61.013410
B. Do, M. L. Stohler, S. Balasubramanian, D. S. Elliott, C. Eash, E. Fischbach, M. A. Fischbach, A. Mills and B. Zwickl, “Experimental Realization of a Quantum Quincunx by Use of Linear Optical Elements,” Journal of the Optical Society of America B, Vol. 22, No. 2, 2005, pp. 499-504. doi:10.1364/JOSAB.22.000499
H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti and Y. Silberberg, “Realization of Quantum Walks with Negligible Decoherence in Waveguide Lattices,” Physical Review Letters, Vol. 100, No. 17, 2008, Article ID: 170506. doi:10.1103/PhysRevLett.100.170506
H. Schmitz, R. Matjeschk, Ch. Schneider, J. Glueckert, M. Enderlein, T. Huber and T. Schaetz, “Quantum Walk of a Trapped Ion in Phase Space,” Physical Review Letters, Vol. 103, No. 9, 2009, Article ID: 090504. doi:10.1103/PhysRevLett.103.090504
F. Zahringer, G. Kirchmair, R. Gerritsma, E. Solano, R. Blatt and C. F. Roos, “Realization of a Quantum Walk with One and Two Trapped Ions,” Physical Review Letters, Vol. 104, No. 10, 2010, Article ID: 100503. doi:10.1103/PhysRevLett.104.100503
K. Karski, L. Foster, J.-M. Choi, A. Steffen, W. Alt, D. Meschede and A. Widera, “Quantum Walk in Position Space with Single Optically Trapped Atoms,” Science, Vol. 325, No. 5937, 2009, pp. 174-177. http://dx.doi.org/10.1126/science.1174436
A. Schreiber, K. N. Cassemiro, V. Potocek, A. Gabris, P. Mosley, E. Andersson, I. Jex and Ch. Silberhorn, “Photons Walking the Line: A Quantum Walk with Adjustable Coin Operations,” Physical Review Letters, Vol. 104, No. 5, 2010, Article ID: 050502. doi:10.1103/PhysRevLett.104.050502
M. A. Broome, A. Fedrizzi, B. P. Lanyon, I. Kassal, A. Aspuru-Guzik and A. G. White, “Discrete Single-Photon Quantum Walks with Tunable Decoherence,” Physical Review Letters, Vol. 104, No. 15, 2010, Article ID: 153602. doi:10.1103/PhysRevLett.104.153602
W. Dur, R. Raussendorf, V. M. Kendon and H. J. Briegel, “Quantum Walks in Optical Lattices,” Physical Review A, Vol. 66, No. 5, 2002, Article ID: 052319. doi:10.1103/PhysRevA.66.052319
K. Eckert, J. Mompart, G. Birkl and M. Lewenstein, “One- and Two-Dimensional Quantum Walks in Arrays of Optical Traps,” Physical Review A, Vol. 72, No. 1, 2005, Article ID: 012327. doi:10.1103/PhysRevA.72.012327
C. M. Chandrashekar, “Implementing the One-Dimensional Quantum (Hadamard) Walk Using a Bose-Einstein Condensate,” Physical Review A, Vol. 74, No. 3, 2006, Article ID: 032307. doi:10.1103/PhysRevA.74.032307
Y. Aharonov, L. Davidovich and N. Zagury, “Quantum Random Walks,” Physical Review A, Vol. 48, No. 2, 1993, pp. 1687-1690. doi:10.1103/PhysRevA.48.1687
A. Ambainis, E. Bach, A. Nayak, A. Vishwanath and J. Watrous, “One Dimensional Quantum Walks with Absorbing Boundaries,” Journal of Computer and System Sciences, Vol. 69, No. 4, 2001, pp. 562-592.
A. Peres, “Separability Criterion for Density Matrices,” Physical Review Letters, Vol. 77, No. 8, 1996, pp. 1413-1415. doi:10.1103/PhysRevLett.77.1413
H. J. Lee, W. Namgung and D. Ahna, “Entanglement Generates Entanglement: Entanglement Transfer by Interaction,” Physical Review A, Vol. 338, No. 3-5, 2005, pp. 192-196. doi:10.1016/j.physleta.2005.03.010
E. Lieb, T. Schultz and D. Mattis, “Two Soluble Models of an Antiferromagnetic Chain,” Annals of Physics, Vol. 16, No. 3, 1961, pp. 407-466. doi:10.1016/0003-4916(61)90115-4
M. Christandl, N. Datta, A. Ekert and Andrew J. Landahl, “Perfect State Transfer in Quantum Spin Networks,” Physical Review Letters, Vol. 92, No. 18, 2004, Article ID: 187902. doi:10.1103/PhysRevLett.92.187902
W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Physical Review Letters, Vol. 80, No. 10, 1998, pp. 2245-2248. doi:10.1103/PhysRevLett.80.2245
T. Oka, N. Konno, R. Arita and H. Aoki, “Breakdown of an Electric-Field Driven System: A Mapping to a Quantum Walk,” Physical Review Letters, Vol. 94, No. 10, 2005, Article ID: 100602. doi:10.1103/PhysRevLett.94.100602
N. Konno, “Localization of an Inhomogeneous Discrete-Time Quantum Walk on the Line,” Quantum Information Processing, Vol. 9, No. 3, 2010, pp. 405-418. doi:10.1007/s11128-009-0147-4
C. M. Chandrashekar, “arXiv: 1001.5326,” 2010.
A. Joye and M. Merkli, “Dynamical Localization of Quantum Walks in Random Environments,” Journal of Statistical Physics, Vol. 140, No. 6, 2010, pp. 1-29. doi:10.1007/s10955-010-0047-0
C. M. Chandrashekar, “Disordered-Quantum-Walk-Induced Localization of a Bose-Einstein Condensate,” Physical Review A, Vol. 83, No. 2, 2011, Article ID: 022320. doi:10.1103/PhysRevA.83.022320
K.-A. Brickman Soderberg, N. Gemelke and C. Chin, “Ultracold Molecules: Vehicles to Scalable Quantum Information Processing,” New Journal of Physics, Vol. 11, 2009, Article ID: 055022. doi:10.1088/1367-2630/11/5/055022
R. Simon and N. Mukunda, “Minimal Three-Component SU(2) Gadget for Polarization Optics,” Physics Letters A, Vol. 143, No. 4-5, 1990, pp. 165-169.