Abstract

We propose and experimentally demonstrate an optimized setup to implement quantum controlled-NOT operation using polarization and orbital angular momentum qubits. This device is more adaptive to inputs with various polarizations, and can work both in classical and quantum single-photon regime. The logic operations performed by such a setup not only possess high stability and polarization-free character, they can also be easily extended to deal with multi-qubit input states. As an example, the experimental implementation of generalized three-qubit Toffoli gate has been presented.

© 2016 Optical Society of America

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References

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2015 (1)

V. Potoček, F. M. Miatto, M. Mirhosseini, O. S. Magaña-Loaiza, A. C. Liapis, D. K. L. Oi, R. W. Boyd, and J. Jeffers, “Quantum Hilbert hotel,” Phys. Rev. Lett. 115(16), 160505 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (1)

I. B. Djordjevic, “Multidimensional QKD based on combined orbital and spin angular momenta of photon,” IEEE Photonics J. 5(6), 7600112 (2013).
[Crossref]

2012 (2)

A. F. Abouraddy, G. Di Giuseppe, T. M. Yarnall, M. C. Teich, and B. E. A. Saleh, “Implementing one-photon three-qubit quantum gates using spatial light modulators,” Phys. Rev. A 86(5), 050303 (2012).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

2010 (3)

2009 (2)

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5(2), 134–140 (2009).
[Crossref]

E. Nagali, F. Sciarrino, F. De Martini, B. Piccirillo, E. Karimi, L. Marrucci, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17(21), 18745–18759 (2009).
[Crossref] [PubMed]

2007 (2)

L.-P. Deng, H. Wang, and K. Wang, “Quantum CNOT gates with orbital angular momentum and polarization of single-photon quantum logic,” J. Opt. Soc. Am. B 24(9), 2517 (2007).
[Crossref]

J. H. Plantenberg, P. C. de Groot, C. J. P. M. Harmans, and J. E. Mooij, “Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits,” Nature 447(7146), 836–839 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (1)

A. N. de Oliveira, S. P. Walborn, and C. H. Monken, “Implementing the Deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B Quantum Semiclassical Opt. 7(9), 288–292 (2005).
[Crossref]

2004 (2)

M. Fiorentino and F. N. Wong, “Deterministic controlled-NOT Gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93(7), 070502 (2004).
[Crossref] [PubMed]

S. Gasparoni, J.-W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93(2), 020504 (2004).
[Crossref] [PubMed]

2003 (9)

J. K. Pachos and P. L. Knight, “Quantum computation with a one-dimensional optical lattice,” Phys. Rev. Lett. 91(10), 107902 (2003).
[Crossref] [PubMed]

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301(5634), 809–811 (2003).
[Crossref] [PubMed]

S. P. Walborn, S. Pádua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68(4), 042313 (2003).
[Crossref]

T. Yamamoto, Y. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, “Demonstration of conditional gate operation using superconducting charge qubits,” Nature 425(6961), 941–944 (2003).
[Crossref] [PubMed]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426(6964), 264–267 (2003).
[Crossref] [PubMed]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature 422(6930), 408–411 (2003).
[Crossref] [PubMed]

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate,” Nature 422(6930), 412–415 (2003).
[Crossref] [PubMed]

Z.-B. Chen, J.-W. Pan, Y.-D. Zhang, C. Brukner, and A. Zeilinger, “All-versus-nothing violation of local realism for two entangled photons,” Phys. Rev. Lett. 90(16), 160408 (2003).
[Crossref] [PubMed]

I. Moreno, G. Paez, and M. Strojnik, “Polarization transforming properties of Dove prisms,” Opt. Commun. 220(4-6), 257–268 (2003).
[Crossref]

2002 (2)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

M. Genovese and C. Novero, “Double entanglement and quantum cryptography,” Eur. Phys. J. D 21(1), 109–113 (2002).
[Crossref]

2001 (2)

B.-G. Englert, C. Kurtsiefer, and H. Weinfurter, “Universal unitary gate for single-photon two-qubit states,” Phys. Rev. A 63(3), 032303 (2001).
[Crossref]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

2000 (1)

J. C. Howell and J. A. Yeazell, “Reducing the complexity of linear optics quantum circuits,” Phys. Rev. A 61(5), 052303 (2000).
[Crossref]

1999 (2)

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Coherent operation of a tunable quantum phase gate in cavity QED,” Phys. Rev. Lett. 83(24), 5166–5169 (1999).
[Crossref]

M. J. Padgett and J. P. Lesso, “Dove prisms and polarized light,” J. Mod. Opt. 46(2), 175–179 (1999).
[Crossref]

1998 (1)

N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57(3), R1477–R1480 (1998).
[Crossref]

1995 (3)

P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, “Simple cavity-QED two-bit universal quantum logic gate: The principle and expected performances,” Phys. Rev. A 52(5), 3554–3559 (1995).
[Crossref] [PubMed]

T. Sleator and H. Weinfurter, “Realizable universal quantum logic gates,” Phys. Rev. Lett. 74(20), 4087–4090 (1995).
[Crossref] [PubMed]

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75(25), 4710–4713 (1995).
[Crossref] [PubMed]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Abouraddy, A. F.

A. F. Abouraddy, G. Di Giuseppe, T. M. Yarnall, M. C. Teich, and B. E. A. Saleh, “Implementing one-photon three-qubit quantum gates using spatial light modulators,” Phys. Rev. A 86(5), 050303 (2012).
[Crossref]

Adami, C.

N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57(3), R1477–R1480 (1998).
[Crossref]

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Almeida, M. P.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5(2), 134–140 (2009).
[Crossref]

Astafiev, O.

T. Yamamoto, Y. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, “Demonstration of conditional gate operation using superconducting charge qubits,” Nature 425(6961), 941–944 (2003).
[Crossref] [PubMed]

Barbieri, M.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nat. Phys. 5(2), 134–140 (2009).
[Crossref]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

Barrett, M.

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate,” Nature 422(6930), 412–415 (2003).
[Crossref] [PubMed]

Becher, C.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature 422(6930), 408–411 (2003).
[Crossref] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Bertet, P.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Coherent operation of a tunable quantum phase gate in cavity QED,” Phys. Rev. Lett. 83(24), 5166–5169 (1999).
[Crossref]

Blatt, R.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature 422(6930), 408–411 (2003).
[Crossref] [PubMed]

Boyd, R. W.

V. Potoček, F. M. Miatto, M. Mirhosseini, O. S. Magaña-Loaiza, A. C. Liapis, D. K. L. Oi, R. W. Boyd, and J. Jeffers, “Quantum Hilbert hotel,” Phys. Rev. Lett. 115(16), 160505 (2015).
[Crossref] [PubMed]

Branning, D.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426(6964), 264–267 (2003).
[Crossref] [PubMed]

Britton, J.

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate,” Nature 422(6930), 412–415 (2003).
[Crossref] [PubMed]

Brukner, C.

Z.-B. Chen, J.-W. Pan, Y.-D. Zhang, C. Brukner, and A. Zeilinger, “All-versus-nothing violation of local realism for two entangled photons,” Phys. Rev. Lett. 90(16), 160408 (2003).
[Crossref] [PubMed]

Brune, M.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Coherent operation of a tunable quantum phase gate in cavity QED,” Phys. Rev. Lett. 83(24), 5166–5169 (1999).
[Crossref]

P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, “Simple cavity-QED two-bit universal quantum logic gate: The principle and expected performances,” Phys. Rev. A 52(5), 3554–3559 (1995).
[Crossref] [PubMed]

Cerf, N. J.

N. J. Cerf, C. Adami, and P. G. Kwiat, “Optical simulation of quantum logic,” Phys. Rev. A 57(3), R1477–R1480 (1998).
[Crossref]

Chen, Z.-B.

Z.-B. Chen, J.-W. Pan, Y.-D. Zhang, C. Brukner, and A. Zeilinger, “All-versus-nothing violation of local realism for two entangled photons,” Phys. Rev. Lett. 90(16), 160408 (2003).
[Crossref] [PubMed]

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

D’Ambrosio, V.

de Groot, P. C.

J. H. Plantenberg, P. C. de Groot, C. J. P. M. Harmans, and J. E. Mooij, “Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits,” Nature 447(7146), 836–839 (2007).
[Crossref] [PubMed]

De Martini, F.

de Oliveira, A. N.

A. N. de Oliveira, S. P. Walborn, and C. H. Monken, “Implementing the Deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B Quantum Semiclassical Opt. 7(9), 288–292 (2005).
[Crossref]

DeMarco, B.

D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate,” Nature 422(6930), 412–415 (2003).
[Crossref] [PubMed]

Deng, L.-P.

Deuschle, T.

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D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, “Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate,” Nature 422(6930), 412–415 (2003).
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S. Gasparoni, J.-W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93(2), 020504 (2004).
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X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301(5634), 809–811 (2003).
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Nat. Photonics (1)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. P. T. Lancaster, T. Deuschle, C. Becher, C. F. Roos, J. Eschner, and R. Blatt, “Realization of the Cirac-Zoller controlled-NOT quantum gate,” Nature 422(6930), 408–411 (2003).
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Opt. Commun. (1)

I. Moreno, G. Paez, and M. Strojnik, “Polarization transforming properties of Dove prisms,” Opt. Commun. 220(4-6), 257–268 (2003).
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Opt. Express (4)

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E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81(5), 052317 (2010).
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S. P. Walborn, S. Pádua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68(4), 042313 (2003).
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V. Potoček, F. M. Miatto, M. Mirhosseini, O. S. Magaña-Loaiza, A. C. Liapis, D. K. L. Oi, R. W. Boyd, and J. Jeffers, “Quantum Hilbert hotel,” Phys. Rev. Lett. 115(16), 160505 (2015).
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Z.-B. Chen, J.-W. Pan, Y.-D. Zhang, C. Brukner, and A. Zeilinger, “All-versus-nothing violation of local realism for two entangled photons,” Phys. Rev. Lett. 90(16), 160408 (2003).
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M. Fiorentino and F. N. Wong, “Deterministic controlled-NOT Gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93(7), 070502 (2004).
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Science (1)

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301(5634), 809–811 (2003).
[Crossref] [PubMed]

Other (4)

D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, 2000).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).

G. Benenti, G. Casati, and G. Strini, Principles of Quantum Computation and Information (World Scientific, 2004).

F. Schlederer, M. Krenn, R. Fickler, M. Malik, and A. Zeilinger, “Cyclic transformation of orbital angular momentum modes,” arXiv preprint arXiv:1512.02696 (2015).

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Figures (4)

Fig. 1
Fig. 1 Schematic of experimental setup for C-NOT gate. BBO: type-Inon-collinear BBO crystal. PBS: polarizing beam splitter. HWP: half-wave plate. BS: 50-50 beam splitter. Filter: frequency filter centered at 780nm with 10nm width. VPP: a flexible vortex phase plate with l=0,1 to verify the outputs’ OAM.
Fig. 2
Fig. 2 Experimental results of the C-NOT gate. (a) Coincidence count rates as a function of the projected output state for a given input state with the single-photon source. (b) The output intensities as a function of the output state for a given input state with the CW laser source.
Fig. 3
Fig. 3 Schematic of experimental setup for generalized Tofolli-gate. The optical elements marked in the figure are identical with those in Fig. 1. The additional vortex phase plate ( l=1 ) is designed to modify the OAM for the subsequent differentiation.
Fig. 4
Fig. 4 Experimental results of the generalized Tofolli-gate. (a) Coincidence count rates as a function of the projected output state for a given input state with the single-photon source. (b) The output intensities as a function of the output state for a given input state with the CW laser source.

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