Quantum walk on the line as an interference phenomenon
Open accessAbstract
We show that the coined quantum walk on a line can be understood as an interference phenomenon, can be classically implemented, and indeed already has been. The walk is essentially two independent walks associated with the different coin sides, coupled only at initiation. There is a simple analogy between the evolution of walker positions and the propagation of light in a dispersive optical fiber.
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The analogy between the wave packets extends beyond the probability distribution to the entanglement between the spinor and spatial degrees of freedom.
“the analogy between the wave packets of (7) and (12) extends beyond the probability distribution to the entanglement between the spinor and spatial degrees of freedom [18].”
From Relativistic quantum walks (2006) · cites this paper as [18]
The paper’s optical-implementation discussion (indexed under Abstract; no page supplied) represents the walk using both frequency and polarization and gives equations for the full state, not just its position probability distribution. It does not discuss entanglement between spinor and spatial degrees of freedom or establish that the citing paper’s two wave packets have analogous entanglement. (LLM, conf=0.78)
Experimental — accuracy not yet measuredSuch localized positive-energy states appear to require entanglement between the spatial and spinor degrees of freedom.
“Such states appear to require entanglement between the spatial and spinor degrees of freedom [18]-this is shown for (7) below.”
From Relativistic quantum walks (2006) · cites this paper as [18]
The discussion of coin-state evolution (indexed as Abstract; page unavailable) says the two sides of the coin evolve independently after an initial coupling. Searches for localized positive-energy states and spatial–spinor entanglement found no passage addressing whether entanglement is required for such states; the paper's discussion of quantum walks does not settle that claim. (LLM, conf=0.76)
Experimental — accuracy not yet measured
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Bru, L. A., Hinarejos, M., Silva, F., de Valcárcel, G. J., & Roldán, E. (2016) · Physical Review A · doi:10.1103/physreva.93.032333 · Cited by 22 · see citing works
Self-citationAttractor-repeller pair of topological zero modes in a nonlinear quantum walk
Gerasimenko, Y., Tarasinski, B., & Beenakker, C. W. J. (2016) · Physical Review A · doi:10.1103/physreva.93.022329 · Cited by 23 · see citing works
Quantum walks: Decoherence and coin-flipping games
Romanelli, A., & Hernández, G. (2010) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2010.12.006 · Cited by 22 · see citing works
Buarque, A. R. C., & Dias, W. S. (2020) · Physical Review A · doi:10.1103/physreva.101.023802 · Cited by 21 · see citing works
Quantum walks in weak electric fields and Bloch oscillations
Arnault, P., Pepper, B., & Pérez, A. (2020) · Physical Review A · doi:10.1103/physreva.101.062324 · Cited by 21 · see citing works
Quantum random walks and wave-packet reshaping at the single-photon level
Ribeiro, P. H. S., Walborn, S. P., Raitz, C., Davidovich, L., & Zagury, N. (2008) · Physical Review A · doi:10.1103/physreva.78.012326 · Cited by 21 · see citing works
Quantum Parrondo's game with random strategies¶
Košík, J., Miszczak, J. A., & Bužek∥, V. (2007) · Journal of Modern Optics · doi:10.1080/09500340701408722 · Cited by 21 · see citing works
Coherent random walks in free space
Eichelkraut, T., Vetter, C., Pérez-Leija, A., Moya-Cessa, H. M., Christodoulides, D. N., & Szameit, A. (2014) · Optica · doi:10.1364/optica.1.000268 · Cited by 20 · see citing works
Quantum walks on the N -cycle subject to decoherence on the coin degree of freedom
Liu, C., & Petulante, N. (2010) · Physical Review E · doi:10.1103/physreve.81.031113 · Cited by 19 · see citing works
Salimi, S. (2008) · International Journal of Theoretical Physics · doi:10.1007/s10773-008-9765-3 · Cited by 20 · see citing works
Quantum walk on the line with quantum rings
Kálmán, O., Kiss, T., & Földi, P. (2009) · Physical Review B · doi:10.1103/physrevb.80.035327 · Cited by 19 · see citing works
Discrete quantum walks and quantum image processing
Venegas-Andraca, S. E. (2005) · Oxford University Research Archive (ORA) (University of Oxford) · doi:10.5287/ora-ov8x0ja0r · Cited by 19 · see citing works
Optical implementation of quantum random walks using weak cross-Kerr media
Wang, C. X., Li, Y., & Hao, L. (2011) · Chinese Science Bulletin · doi:10.1007/s11434-011-4545-5 · Cited by 18 · see citing works
- Authors
- Knight, P. L., Roldán, E., & Sipe, J. E.
- Affiliations
- Imperial College London (GB)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2003-08-27
- Volume
- 68
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1988086028
- Cited by
- 176
- References
- 16
- Citations by year
- 2025: 1 · 2024: 5 · 2022: 5 · 2021: 11 · 2020: 11 · 2019: 9 · 2018: 7 · 2017: 7 · 2016: 5 · 2015: 8 · 2014: 4 · 2013: 12 · 2012: 12
- FWCI
- 9.55
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Spiral (Imperial College London) (submittedVersion)
- arXiv (Cornell University)
- Funders
- European Commission
- Natural Sciences and Engineering Research Council of Canada
- Engineering and Physical Sciences Research Council
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- discrete-time quantum walks, interference, coin operator
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