The role of coherence on two-particle quantum
walks

• Authors: Li-Hua Lu , Shan Zhu , You-Quan Li
• Languages of publication: EN

Abstracts

EN

We investigate the dynamical properties of the
two-boson quantum walk in systems with different degrees
of coherence, and where the effect of the coherence
on the two-boson quantum walk can be naturally introduced.
A general analytical expression for the two-boson
correlation function, for both pure states and mixed states,
is given.We propose a possible two-photon quantum-walk
scheme with a mixed initial state, and find that the twophoton
correlation function and the average distance between
two photons can be influenced by the initial photon
distribution, the relative phase, or the degree of coherence.
The propagation features of our numerical results can be
explained by our analytical two-photon correlation function.

Keywords

EN

wo-particle quantum walk; degree of coherence; two-photon correlation function; pure state; mixedstate

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2015
• Volume: 13
• Issue: 1

Dates

accepted

13 - 10 - 2015

online

25 - 11 - 2015

received

6 - 2 - 2015

Contributors

author

Li-Hua Lu

• Zhejiang Institute of Modern Physics and Department of
  Physics, Zhejiang University, Hangzhou 310027, P. R. China

author

Shan Zhu

• Zhejiang Institute of Modern Physics and Department of
  Physics, Zhejiang University, Hangzhou 310027, P. R. China
• Collaborative Innovation Center of Advanced Microstructures,
  Nanjing, P. R. China

author

You-Quan Li

• Zhejiang Institute of Modern Physics and Department of
  Physics, Zhejiang University, Hangzhou 310027, P. R. China
• Collaborative Innovation Center of Advanced Microstructures,
  Nanjing, P. R. China

References

• [1] Y. Aharonov, L. Davidovich, and N. Zagury: "Quantum randomwalks" Phys. Rev. A, Vol. 48, (1993), PP. 1687.Y. Aharonov, L. Davidovich, and N. Zagury: "Quantum randomwalks", Phys. Rev. A, Vol. 48, (1993), PP. 1687.
• [2] M. Mohseni, P. Rebentrost, S. Lloyd, and A. Aspuru-Guzik:"Environment-assisted quantum walks in photosynthetic energytransfer", J. Chem. Phys., Vol. 129, (2008), PP. 174106.[WoS]
• [3] N. Shenvi, J. Kempe, and R.B. Whaley: "Quantum random-walksearch algorithm", Phys. Rev. A, Vol. 67, (2003), PP. 052307.
• [4] S. E. Venegas-Andraca: "Quantum walks: a comprehensive review", Quantum Information Processing, Vol. 11, (2012), PP.1015.
• [5] M. S. Underwood and D.L. Feder: "Universal quantum computationby discontinuous quantum walk", Phys. Rev. A, Vol. 82,(2010), PP. 042304.
• [6] N.B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon:"Universal quantumcomputation using the discrete-time quantumwalk", Phys. Rev. A, Vol. 81, (2010), PP. 042330.
• [7] A.M. Childs: "Universal Computation by Quantum Walk", Phys.Rev. Lett., Vol. 102, (2009), PP. 180501.[WoS]
• [8] A. M. Childs, D. Gosset, Z. Webb: "Universal Computation byMultiparticle QuantumWalk ", Science, Vol. 339, (2013), PP. 791.
• [9] J. Watrous: "Quantum simulations of classical random walksand undirected graph connectivity", Journal of computer andsystem sciences, Vol. 62, (2001), PP. 376.
• [10] E. Farhi and S. Gutmann: "Quantum computation and decisiontrees", Phys. Rev. A, Vol. 58, (1998), PP. 915.
• [11] H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y.Silberberg: "Realization of Quantum Walks with Negligible Decoherencein Waveguide Lattices", Phys. Rev. Lett., Vol. 100,(2008), PP. 170506.[WoS]
• [12] A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, P. J. Mosley,E. Andersson, I. Jex, and Ch. Silberhorn: "Photons Walking theLine: A Quantum Walk with Adjustable Coin Operations", Phys.Rev. Lett., Vol. 104, (2010), PP. 050502.[WoS]
• [13] M. A. Broome, A. Fedrizzi, B. P. Lanyon, I. Kassal, A. Aspuru-Guzik, and A. G. White: "Discrete Single-Photon QuantumWalkswith Tunable Decoherence", Phys. Rev. Lett., Vol. 104, (2010),PP. 153602.
• [14] M. Karski,L. Förster, J. M. Choi, A. Steffen, W. Alt, D. Meschede,A. Widera: "Quantum Walk in Position Space with Single OpticallyTrapped Atoms ", Science, Vol. 325, (2009), PP. 174.[WoS]
• [15] C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauss,T. Fukuhara, I. Bloch, S. Kuhr: " Single-spin addressing in anatomic Mott insulator ", Nature, Vol. 471, (2011), PP. 319.[WoS]
• [16] Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg: "Quantumand Classical Correlations in Waveguide Lattices", Phys.Rev. Lett., Vol. 102, (2009), PP. 253904.[WoS]
• [17] A. Peruzzo, M. Lobino, J. C. F.Matthews, N.Matsuda, A. Politi, K.Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg,Y. Silberberg, M. G. Thompson, J. L. Obrien: "Quantum Walks ofCorrelated Photons ", Science, Vol. 329,(2010), PP. 1500.[WoS]
• [18] P. L. Knight, E. Roldan, J. E. Sipe: "Quantum walk on the line asan interference phenomenon", Phys. Rev. A, Vol. 68, (2003), PP.020301.
• [19] Y.Omar, N. Paunkovic, L. Sheridan, S. Bose: "Quantumwalk on aline with two entangled particles", Phys. Rev. A, Vol. 74, (2006),PP. 042304.
• [20] Y. Lahini, M. Verbin, S. D. Huber, Y. Bromberg, R. Pugatch, andY. Silberberg: "Quantum walk of two interacting bosons", Phys.Rev. A, Vol. 86, (2012), PP. 011603.[WoS]
• [21] X. Z. Qin, Y. G. Ke, X. W. Guan, Z. B. Li, N. Andrei, and C. H.Lee: "QuantumWalks of Two Interacting Particles in One Dimension",Phys. Rev. A, Vol. 90, (2014), PP. 062301.
• [22] V. Kendon:"Decoherence in quantum walks - A review", Mathematicalstructures in computer science, Vol. 17, (2007), PP. 1169.
• [23] E. Farhi, and S. Gutmann:"Quantum computation and decisiontrees", Phys. Rev. A, Vol. 58, (1997), PP. 915.
• [24] Z. J. Li, J. A. Izaac, and J. B. Wang: "Position-defect-inducedreflection, trapping, transmission, and resonance in quantumwalks", Phys. Rev. A, Vol. 87, (2013), PP. 012314.[WoS]
• [25] K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, M. Zukowski:"Noncalssical statistics at multiport beam-splitters", Appl.Phys. B, Vol. 60, (1995), PP. S111.
• [26] F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto,M. Segev, and Y. Silberberg: "Discrete solitons in optics", Phys.Rep., Vol. 463, (2008), PP. 1.
• [27] A. Yariv: Quantum Electronics, Wiley, New York, (1989).
• [28] A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tunnermann,and F. Lederer: "Quasi-incoherent propagation in waveguide arrays",Appl. Phys. Lett., Vol. 90, (2007), PP. 241113.[WoS]
• [29] L. H. Lu and Y. Q. Li: "Dynamics for partially coherent Bose-Einstein condensates in double wells", Phys. Rev. A, Vol. 80,(2009), PP. 033619.
• [30] R. Hanbury Brown and R. Q. Twiss: "Correlation between photonsin 2 coherent beams of light", Nature, Vol. 177, (1956), PP.27.
• [31] J. Schachenmayer, B. P. Lanyon, C. F. Roos, and A. J. Daley: "Entanglementgrowth in quench dynamics with variable range interactions",Phys. Rev. X, Vol. 3, (2013), PP. 031015.[WoS]

Identifiers

DOI

10.1515/phys-2015-0042