Abstract

Quantum random walks (QRWs) are random processes in which the resulting probability density of the “walker” state, whose movement is governed by a “coin” state, is described in a nonclassical manner. Previously, Q-plates have been used to demonstrate QRWs with polarization and orbital angular momentum playing the roles of coin and walker states, respectively. In this theoretical analysis, we show how stress-engineered optics can be used to develop new platforms for complex QRWs through relatively simple optical elements. Our work opens up new paths to speed up classical-to-quantum transitions in robust photonic networks.

© 2019 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Polarization singularities in a stress-engineered optic

Ashan Ariyawansa, Kevin Liang, and Thomas G. Brown
J. Opt. Soc. Am. A 36(3) 312-319 (2019)

Quantum random walks in a coherent atomic system via electromagnetically induced transparency

Yun Li, Chao Hang, Lei Ma, Weiping Zhang, and Guoxiang Huang
J. Opt. Soc. Am. B 25(12) C39-C45 (2008)

Quantum random walks with multiphoton interference and high-order correlation functions

Bryan T. Gard, Robert M. Cross, Petr M. Anisimov, Hwang Lee, and Jonathan P. Dowling
J. Opt. Soc. Am. B 30(6) 1538-1545 (2013)

References

  • View by:
  • |
  • |
  • |

  1. Y. Aharonov, L. Davidovich, and N. Zagury, “Quantum random walks,” Phys. Rev. A 48, 1687 (1993).
    [Crossref]
  2. B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).
  3. F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
    [Crossref]
  4. B. C. Travaglione and G. J. Milburn, “Implementing the quantum random walk,” Phys. Rev. A 65, 032310 (2002).
    [Crossref]
  5. J. Kempe, “Quantum random walks-an introductory overview,” arXiv:quant-ph/0303081 (2008).
  6. H. Jeong, M. Paternostro, and M. S. Kim, “Simulation of quantum random walks using the interference of a classical field,” Phys. Rev. A 69, 012310 (2004).
    [Crossref]
  7. S. M. H. Rafsanjani, M. Mirhosseini, O. S. Magaña-Loaiza, and R. W. Boyd, “State transfer based on classical nonseparability,” Phys. Rev. A 92, 023827 (2015).
    [Crossref]
  8. A. M. Childs, “Universal computation by quantum walk,” Phys. Rev. Lett. 102, 180501 (2009).
    [Crossref]
  9. N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81, 042330 (2010).
    [Crossref]
  10. A. M. Childs, D. Gosset, and Z. Webb, “Universal computation by multiparticle quantum walk,” Science 339, 791–794 (2013).
    [Crossref]
  11. A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18, 10777–10785 (2010).
    [Crossref]
  12. A. K. Spilman and T. G. Brown, “Stress birefringent, space-variant wave plates for vortex illumination,” Appl. Opt. 46, 61–66 (2007).
    [Crossref]
  13. R. D. Ramkhalawon, T. G. Brown, and M. A. Alonso, “Imaging the polarization of a light field,” Opt. Express 21, 4106–4115 (2013).
    [Crossref]
  14. B. G. Zimmerman, R. Ramkhalawon, M. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
    [Crossref]
  15. S. Sivankutty, E. R. Andresen, G. Bouwmans, T. G. Brown, M. A. Alonso, and H. Rigneault, “Single-shot polarimetry imaging of multicore fiber,” Opt. Lett. 41, 2105–2108 (2016).
    [Crossref]
  16. A. K. Spilman and T. G. Brown, “Stress-induced focal splitting,” Opt. Express 15, 8411–8421 (2007).
    [Crossref]
  17. A. Ariyawansa and T. G. Brown, “Oblique propagation of light through a thick, space-variant birefringent element,” Opt. Express 26, 18832–18841 (2018).
    [Crossref]
  18. A. Ariyawansa, K. Liang, and T. G. Brown, “Polarization singularities in a stress-engineered optic,” J. Opt. Soc. Am. A 36, 312–319 (2019).
    [Crossref]
  19. J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
    [Crossref]
  20. A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, and I. A. Walmsley, “Distinguishability and many-particle interference,” Phys. Rev. Lett. 118, 153603 (2017).
    [Crossref]
  21. O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
    [Crossref]

2019 (2)

A. Ariyawansa, K. Liang, and T. G. Brown, “Polarization singularities in a stress-engineered optic,” J. Opt. Soc. Am. A 36, 312–319 (2019).
[Crossref]

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

2018 (1)

2017 (1)

A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, and I. A. Walmsley, “Distinguishability and many-particle interference,” Phys. Rev. Lett. 118, 153603 (2017).
[Crossref]

2016 (1)

2015 (2)

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

S. M. H. Rafsanjani, M. Mirhosseini, O. S. Magaña-Loaiza, and R. W. Boyd, “State transfer based on classical nonseparability,” Phys. Rev. A 92, 023827 (2015).
[Crossref]

2014 (1)

B. G. Zimmerman, R. Ramkhalawon, M. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
[Crossref]

2013 (3)

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

R. D. Ramkhalawon, T. G. Brown, and M. A. Alonso, “Imaging the polarization of a light field,” Opt. Express 21, 4106–4115 (2013).
[Crossref]

A. M. Childs, D. Gosset, and Z. Webb, “Universal computation by multiparticle quantum walk,” Science 339, 791–794 (2013).
[Crossref]

2010 (2)

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express 18, 10777–10785 (2010).
[Crossref]

N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81, 042330 (2010).
[Crossref]

2009 (1)

A. M. Childs, “Universal computation by quantum walk,” Phys. Rev. Lett. 102, 180501 (2009).
[Crossref]

2007 (2)

2004 (1)

H. Jeong, M. Paternostro, and M. S. Kim, “Simulation of quantum random walks using the interference of a classical field,” Phys. Rev. A 69, 012310 (2004).
[Crossref]

2002 (1)

B. C. Travaglione and G. J. Milburn, “Implementing the quantum random walk,” Phys. Rev. A 65, 032310 (2002).
[Crossref]

1993 (1)

Y. Aharonov, L. Davidovich, and N. Zagury, “Quantum random walks,” Phys. Rev. A 48, 1687 (1993).
[Crossref]

Aharonov, Y.

Y. Aharonov, L. Davidovich, and N. Zagury, “Quantum random walks,” Phys. Rev. A 48, 1687 (1993).
[Crossref]

Alonso, M.

B. G. Zimmerman, R. Ramkhalawon, M. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
[Crossref]

Alonso, M. A.

Andresen, E. R.

Ariyawansa, A.

Barbieri, M.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Barz, S.

A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, and I. A. Walmsley, “Distinguishability and many-particle interference,” Phys. Rev. Lett. 118, 153603 (2017).
[Crossref]

Beckley, A. M.

Bouwmans, G.

Boyd, R. W.

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

S. M. H. Rafsanjani, M. Mirhosseini, O. S. Magaña-Loaiza, and R. W. Boyd, “State transfer based on classical nonseparability,” Phys. Rev. A 92, 023827 (2015).
[Crossref]

Brown, T. G.

Busch, K.

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

Cardano, F.

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

Childs, A. M.

A. M. Childs, D. Gosset, and Z. Webb, “Universal computation by multiparticle quantum walk,” Science 339, 791–794 (2013).
[Crossref]

A. M. Childs, “Universal computation by quantum walk,” Phys. Rev. Lett. 102, 180501 (2009).
[Crossref]

Cooper, S.

N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81, 042330 (2010).
[Crossref]

Datta, A.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Davidovich, L.

Y. Aharonov, L. Davidovich, and N. Zagury, “Quantum random walks,” Phys. Rev. A 48, 1687 (1993).
[Crossref]

de Lisio, C.

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

Dudley, A.

B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).

Everitt, M.

N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81, 042330 (2010).
[Crossref]

Forbes, A.

B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).

Gates, J. C.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Gerrits, T.

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

Gosset, D.

A. M. Childs, D. Gosset, and Z. Webb, “Universal computation by multiparticle quantum walk,” Science 339, 791–794 (2013).
[Crossref]

Goyal, S.

B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).

Humphreys, P. C.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Jeong, H.

H. Jeong, M. Paternostro, and M. S. Kim, “Simulation of quantum random walks using the interference of a classical field,” Phys. Rev. A 69, 012310 (2004).
[Crossref]

Jin, X.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Jones, A. E.

A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, and I. A. Walmsley, “Distinguishability and many-particle interference,” Phys. Rev. Lett. 118, 153603 (2017).
[Crossref]

Karimi, E.

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

Kempe, J.

J. Kempe, “Quantum random walks-an introductory overview,” arXiv:quant-ph/0303081 (2008).

Kendon, V.

N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81, 042330 (2010).
[Crossref]

Kim, M. S.

H. Jeong, M. Paternostro, and M. S. Kim, “Simulation of quantum random walks using the interference of a classical field,” Phys. Rev. A 69, 012310 (2004).
[Crossref]

Kolthammer, W. S.

A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, and I. A. Walmsley, “Distinguishability and many-particle interference,” Phys. Rev. Lett. 118, 153603 (2017).
[Crossref]

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Konrad, T.

B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).

Kundys, D.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Langford, N. K.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

León-Montiel, R. de. J.

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

Liang, K.

Lita, A. E.

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

Lovett, N. B.

N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81, 042330 (2010).
[Crossref]

Magaña-Loaiza, O. S.

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

S. M. H. Rafsanjani, M. Mirhosseini, O. S. Magaña-Loaiza, and R. W. Boyd, “State transfer based on classical nonseparability,” Phys. Rev. A 92, 023827 (2015).
[Crossref]

Marrucci, L.

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).

Menssen, A. J.

A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, and I. A. Walmsley, “Distinguishability and many-particle interference,” Phys. Rev. Lett. 118, 153603 (2017).
[Crossref]

Metcalf, B. J.

A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, and I. A. Walmsley, “Distinguishability and many-particle interference,” Phys. Rev. Lett. 118, 153603 (2017).
[Crossref]

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Milburn, G. J.

B. C. Travaglione and G. J. Milburn, “Implementing the quantum random walk,” Phys. Rev. A 65, 032310 (2002).
[Crossref]

Mirhosseini, M.

S. M. H. Rafsanjani, M. Mirhosseini, O. S. Magaña-Loaiza, and R. W. Boyd, “State transfer based on classical nonseparability,” Phys. Rev. A 92, 023827 (2015).
[Crossref]

Mirin, R. P.

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

Nam, S. W.

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

Padgett, M.

B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).

Paparo, D.

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

Paternostro, M.

H. Jeong, M. Paternostro, and M. S. Kim, “Simulation of quantum random walks using the interference of a classical field,” Phys. Rev. A 69, 012310 (2004).
[Crossref]

Perez-Leija, A.

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

Qassim, F. M. H.

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

Rafsanjani, S. M. H.

S. M. H. Rafsanjani, M. Mirhosseini, O. S. Magaña-Loaiza, and R. W. Boyd, “State transfer based on classical nonseparability,” Phys. Rev. A 92, 023827 (2015).
[Crossref]

Ramkhalawon, R.

B. G. Zimmerman, R. Ramkhalawon, M. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
[Crossref]

Ramkhalawon, R. D.

Rigneault, H.

Romanato, F.

B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).

Roux, F.

B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).

Ruffato, G.

B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).

Santamato, E.

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

Sciarrino, F.

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

Sephton, B.

B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).

Sivankutty, S.

Slussarkenko, S.

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

Smith, B. J.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Smith, P. G. R.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Spilman, A. K.

Spring, J. B.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Thomas-Peter, N.

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Tichy, M. C.

A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, and I. A. Walmsley, “Distinguishability and many-particle interference,” Phys. Rev. Lett. 118, 153603 (2017).
[Crossref]

Travaglione, B. C.

B. C. Travaglione and G. J. Milburn, “Implementing the quantum random walk,” Phys. Rev. A 65, 032310 (2002).
[Crossref]

Trevers, M.

N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81, 042330 (2010).
[Crossref]

U’Ren, A. B.

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

Walmsley, I. A.

A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, and I. A. Walmsley, “Distinguishability and many-particle interference,” Phys. Rev. Lett. 118, 153603 (2017).
[Crossref]

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

Webb, Z.

A. M. Childs, D. Gosset, and Z. Webb, “Universal computation by multiparticle quantum walk,” Science 339, 791–794 (2013).
[Crossref]

You, C.

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

Zagury, N.

Y. Aharonov, L. Davidovich, and N. Zagury, “Quantum random walks,” Phys. Rev. A 48, 1687 (1993).
[Crossref]

Zimmerman, B. G.

B. G. Zimmerman, R. Ramkhalawon, M. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
[Crossref]

Appl. Opt. (1)

J. Opt. Soc. Am. A (1)

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (5)

Y. Aharonov, L. Davidovich, and N. Zagury, “Quantum random walks,” Phys. Rev. A 48, 1687 (1993).
[Crossref]

B. C. Travaglione and G. J. Milburn, “Implementing the quantum random walk,” Phys. Rev. A 65, 032310 (2002).
[Crossref]

H. Jeong, M. Paternostro, and M. S. Kim, “Simulation of quantum random walks using the interference of a classical field,” Phys. Rev. A 69, 012310 (2004).
[Crossref]

S. M. H. Rafsanjani, M. Mirhosseini, O. S. Magaña-Loaiza, and R. W. Boyd, “State transfer based on classical nonseparability,” Phys. Rev. A 92, 023827 (2015).
[Crossref]

N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, “Universal quantum computation using the discrete-time quantum walk,” Phys. Rev. A 81, 042330 (2010).
[Crossref]

Phys. Rev. Lett. (2)

A. M. Childs, “Universal computation by quantum walk,” Phys. Rev. Lett. 102, 180501 (2009).
[Crossref]

A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, and I. A. Walmsley, “Distinguishability and many-particle interference,” Phys. Rev. Lett. 118, 153603 (2017).
[Crossref]

Proc. SPIE (1)

B. G. Zimmerman, R. Ramkhalawon, M. Alonso, and T. G. Brown, “Pinhole array implementation of star test polarimetry,” Proc. SPIE 8949, 894912 (2014).
[Crossref]

Quantum Inf. (1)

O. S. Magaña-Loaiza, R. de. J. León-Montiel, A. Perez-Leija, A. B. U’Ren, C. You, K. Busch, A. E. Lita, S. W. Nam, R. P. Mirin, and T. Gerrits, “Multiphoton quantum-state engineering using conditional measurements,” Quantum Inf. 5, 80 (2019).
[Crossref]

Sci. Adv. (1)

F. Cardano, F. M. H. Qassim, E. Karimi, S. Slussarkenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, R. W. Boyd, and L. Marrucci, “Quantum walks and wavepacket dynamics on a lattice with twisted photons,” Sci. Adv. 1, e1500087 (2015).
[Crossref]

Science (2)

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

A. M. Childs, D. Gosset, and Z. Webb, “Universal computation by multiparticle quantum walk,” Science 339, 791–794 (2013).
[Crossref]

Other (2)

J. Kempe, “Quantum random walks-an introductory overview,” arXiv:quant-ph/0303081 (2008).

B. Sephton, A. Dudley, G. Ruffato, F. Romanato, L. Marrucci, M. Padgett, S. Goyal, F. Roux, T. Konrad, and A. Forbes, “A versatile quantum walk resonator with bright classical light,” arXiv:1810.06850 (2018).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1. In a three-step process, a metal ring (with material removed symmetrically from the inner edge) is heated, BK7 glass is placed within the ring, and the metal ring is allowed to cool. The resulting compression of the BK7 from thermal cooling gives rise to a pattern of stress-induced birefringence.
Fig. 2.
Fig. 2. After a uniform LHC electric field passes through a tilted SEO, the resulting intensity of the RHC component of the output beam (shown in this figure along with spatially varying polarization ellipses) exhibits several optical (and polarization) vortices.
Fig. 3.
Fig. 3. Illustration of the experimental implementation of QRW with SEOs. The initial field $ {\vec E_i} $ goes through $ N $ copies of $ \hat Z $, which is composed of an SEO and a waveplate (either a QWP or a HWP). Note that it is necessary to include wave plates within each $ \hat Z $ along with the SEO in order to generate QRWs.
Fig. 4.
Fig. 4. These plots show $ \int_0^1 |{Z_\textit{ij}}{|^2}\rho {\rm d}\rho $, over possible OAM values ($ N = 20 $) for various values of $ c $ in an identity QRW process. Parts (a)–(d) correspond to $ {Z_{11}},{Z_{12}},{Z_{21}}, $ and $ {Z_{22}} $, respectively. Note that every plot shown here approaches, in an oscillatory manner, an asymptotic value as $ c $ gets large [as indicated by Eq. (12)].
Fig. 5.
Fig. 5. These plots show $ |{Z_\textit{ij}}{|^2} $ for $ N = 20 $ and the identity QRW. Appendix A shows that $ {Z_{12}} = {Z_{21}} $ and so only $ |{Z_{12}}{|^2} $ is shown. Furthermore, the off-diagonal elements of $ {\hat Z^N} $ contain only terms proportional to $ {e^{{\rm i}(2r + 1)\phi }} $, where $ r $ takes integer values in the range $ [ - N/2,N/2] $; that is, they only contain odd-valued OAM terms. Conversely, the diagonal elements contain terms proportional $ {e^{{\rm i}2r\phi }} $. The first and second rows correspond to $ c = 4\pi $ and $ c = \pi /3 $, respectively. The gray region marks the region within the aperture. As $ r $ goes from $ - N/2 $ to 0, the functions spread out; this behavior is particularly relevant for the low $ c $ regime. Although the range of $ r \in [0,N/2] $ is not shown explicitly, the behavior of $ {Z_\textit{ij}} $ around $ r = 0 $ is symmetric, with the caveat of $ {Z_{11}} $ and $ {Z_{22}} $ swapping roles.
Fig. 6.
Fig. 6. $ {\mathcal P}(m)$ for the value of OAM after $ N $ iterations of the SEO identity QRW process, with $ c = 4\pi $. (a) and (b) correspond to the LHC and RHC of $ {\vec E_{\rm f}} $ for a symmetric input field given by $ {\vec E_{\rm i}} = {E_0}(1 \,1) $. (c) and (d) correspond to the LHC and RHC of $ {\vec E_{\rm f}} $ for an asymmetric input field given by $ {\vec E_{\rm i}} = {E_0}(1 \,0) $. The analogous plots of a Q-plate would have only nonzero probabilities for the extreme-most values of OAM ($ m = \pm N $).
Fig. 7.
Fig. 7. $ {\mathcal P}(m)$ for the value of OAM after $ N $ iterations of the SEO Hadamard QRW process, with $ c = 4\pi $. (a) and (b) correspond to the LHC and RHC of $ {\vec E_{\rm f}} $ for a symmetric input field given by $ {\vec E_{\rm i}} = {E_0}(1 \,1) $. (c) and (d) correspond to the LHC and RHC of $ {\vec E_{\rm f}} $ for an asymmetric input field given by $ {\vec E_{\rm i}} = {E_0}(1 \,0) $.
Fig. 8.
Fig. 8. $ {\mathcal P}(m)$ for the value of OAM after $ N $ iterations of the Hadamard QRW process, for a Q-plate with $ q = 1/2 $. (a) and (b) correspond to the LHC and RHC of $ {\vec E_{\rm f}} $ for a symmetric input field given by $ {\vec E_{\rm i}} = {E_0}(1 \,1) $. (c) and (d) correspond to the LHC and RHC of $ {\vec E_{\rm f}} $ for an asymmetric input field given by $ {\vec E_{\rm i}} = {E_0}(1 \,0) $.
Fig. 9.
Fig. 9. Variances, as a function of $ N $, of the probability mass function $ {\mathcal P}(m)$ associated with various RW processes. For the QRWs, the opaque and translucent curves correspond to the LHC and RHC components of the output beam, respectively. Furthermore, the solid and dashed curves correspond to $ {\vec E_{\rm i}} = {E_0}(1 \,1) $ and $ {E_0}(1 \,0) $, respectively. It should be noted that, although not shown here, the identity QRW with the Q-plate gives the largest variances.
Fig. 10.
Fig. 10. $ {\mathcal P}(m)$ for the value of OAM after $ N $ iterations of the SEO identity QRW process, with $ c = \pi /3 $. (a) and (b) correspond to the LHC and RHC of $ {\vec E_{\rm f}} $ for a symmetric input field given by $ {\vec E_{\rm i}} = {E_0}(1 \,1) $. (c) and (d) correspond to the LHC and RHC of $ {\vec E_{\rm f}} $ for an asymmetric input field given by $ {\vec E_{\rm i}} = {E_0}(1 \,0) $.
Fig. 11.
Fig. 11. $ {\mathcal P}(m)$ for the value of OAM after $ N $ iterations of the SEO Hadamard QRW process, with $ c = \pi /3 $. (a) and (b) correspond to the LHC and RHC of $ {\vec E_{\rm f}} $ for a symmetric input field given by $ {\vec E_{\rm i}} = {E_0}(1 \,1) $. (c) and (d) correspond to the LHC and RHC of $ {\vec E_{\rm f}} $ for an asymmetric input field given by $ {\vec E_{\rm i}} = {E_0}(1 \,0) $.

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

J ^ S E O = [ cos [ Δ ( ρ ) ] i e i ϕ sin [ Δ ( ρ ) ] i e i ϕ sin [ Δ ( ρ ) ] cos [ Δ ( ρ ) ] ] ,
J ^ Q = [ 0 i e i 2 q ϕ i e i 2 q ϕ 0 ] ,
J ^ Q W P ( θ ) = 1 2 [ 1 i e i 2 θ i e i 2 θ 1 ]
J ^ H W P ( θ ) = i [ 0 e i 2 θ e i 2 θ 0 ] ,
Z ^ I = J ^ H W P ( 0 ) J ^ S E O ,
Z ^ H = J ^ Q W P ( π / 4 ) J ^ S E O ,
E f ( ρ , ϕ ) = Z ^ N E i ( ρ , ϕ ) ,
E f ( ρ , ϕ ) = m = α n ( ρ ) e i m ϕ [ 1 0 ] + m = β n ( ρ ) e i m ϕ [ 0 1 ] ,
P ( m ) = 1 μ 0 1 ρ | α m ( ρ ) | 2 d ρ ,
μ = m = 0 1 ρ | α m ( ρ ) | 2 d ρ
Z ^ N = [ Z 11 ( N , ρ , ϕ ) Z 12 ( N , ρ , ϕ ) Z 21 ( N , ρ , ϕ ) Z 22 ( N , ρ , ϕ ) ] = [ m Z 11 ( N , m , ρ ) e i m ϕ m Z 12 ( N , m , ρ ) e i m ϕ m Z 21 ( N , m , ρ ) e i m ϕ m Z 22 ( N , m , ρ ) e i m ϕ ] ,
lim T 0 0 1 | f ( ρ / T ) | 2 d ρ 0 1 | f ( ρ ) | 2 d ρ .
Z ^ N = λ 2 λ 1 N λ 1 λ 2 N λ 2 λ 1 I ^ + λ 2 N λ 1 N λ 2 λ 1 Z ^ ,
Z 11 ( N , ρ , ϕ ) = r { A N , r ( ρ , θ ) + e i 2 θ sin [ Δ ( ρ ) ] × A N + 1 , r + 1 / 2 ( ρ , θ ) } e i 2 r ϕ ,
Z 12 ( N , ρ , ϕ ) = r { i e i 2 θ cos [ Δ ( ρ ) ] × A N + 1 , r + 1 / 2 ( ρ , θ ) } e i ( 2 r + 1 ) ϕ ,
Z 21 ( N , ρ , ϕ ) = r { i e i 2 θ cos [ Δ ( ρ ) ] × A N + 1 , r + 1 / 2 ( ρ , θ ) } e i ( 2 r + 1 ) ϕ ,
Z 22 ( N , ρ , ϕ ) = r { A N , r ( ρ , θ ) + e i 2 θ sin [ Δ ( ρ ) ] × A N + 1 , r 1 / 2 ( ρ , θ ) } e i 2 r ϕ .
A N , l , q , p ( ρ , θ ) = [ ( n 2 l + 1 ) ( n 2 l ) ] ( l q ) ( n 2 q p ) × ( 1 ) n + q + 1 2 n 2 q sin n 2 q [ Δ ( ρ ) ] e i 2 [ n 2 ( q + p ) ] θ .
A N , r ( ρ , θ ) = s = 0 N / 2 j = 0 M i n [ s , N ( | 2 r | 1 ) 2 ] A N , s , j , r + N / 2 j ( ρ ) .
Z 11 ( N , ρ , ϕ ) = r ( B N , r ( ρ , θ ) + e i r ϕ 2 { cos [ Δ ( ρ ) ] D N , r e i 2 θ sin [ Δ ( ρ ) ] D N , r + 1 } ) ,
Z 12 ( N , ρ , ϕ ) = r e i r ϕ 2 { i e i 2 θ cos [ Δ ( ρ ) ] D N , r + i sin [ Δ ( ρ ) ] D N , r 1 } ,
Z 21 ( N , ρ , ϕ ) = r e i r ϕ 2 { i e i 2 θ cos [ Δ ( ρ ) ] D N , r + i sin [ Δ ( ρ ) ] D N , r + 1 } ,
Z 22 ( N , ρ , ϕ ) = r ( B N , r ( ρ , θ ) + e i r ϕ 2 { cos [ Δ ( ρ ) ] D N , r e i 2 θ sin [ Δ ( ρ ) ] D N , r 1 } ) .
B N , l , q , p , y ( ρ , θ ) = [ ( n 2 l + 1 ) ( n 2 l ) ] ( l q ) ( n 2 q p ) × ( p y ) ( 1 ) 2 n q p + 1 2 n 2 q + 2 p cos n 2 q p [ Δ ( ρ ) ] × sin p [ Δ ( ρ ) ] e i 2 ( p 2 y ) θ ,
D N , l , q , p , y ( ρ , θ ) = ( n 2 l + 1 ) ( l q ) ( n ( 2 q + 1 ) p ) ( p y ) × ( 1 ) 2 n q p 2 n ( 2 q + 1 ) + 2 p cos n ( 2 q + 1 ) p [ Δ ( ρ ) ] × sin p [ Δ ( ρ ) ] e i 2 ( p 2 y ) θ .
B N , r ( ρ , θ ) = l = 0 N / 2 q = 0 l p = 0 n 2 q y = 0 p B N , l , q , p , y ( ρ , θ ) δ r p 2 y ,
D N , r ( ρ , θ ) = l = 0 N / 2 q = 0 l p = 0 N ( 2 q + 1 ) y = 0 p D N , l , q , p , y ( ρ , θ ) δ r p 2 y ,

Metrics