Abstract

We propose a multidimensional quantum information encoding approach based on temporal modulation of single photons, where the Hilbert space can be spanned by an in-principle infinite set of orthonormal temporal profiles. We analyze two specific realizations of such modulation schemes, and show that error rate per symbol can be smaller than 1% for practical implementations. Temporal modulation may enable multidimensional quantum communication over the existing fiber optical infrastructure, as well as provide an avenue for probing high-dimensional entanglement approaching the continuous limit.

© 2012 OSA

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  1. J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
    [CrossRef]
  2. J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95(26), 260501 (2005).
    [CrossRef] [PubMed]
  3. T. Vértesi, S. Pironio, and N. Brunner, “Closing the detection loophole in bell experiments using qudits,” Phys. Rev. Lett. 104(6), 060401 (2010).
    [CrossRef] [PubMed]
  4. J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. 64(21), 2495–2498 (1990).
    [CrossRef] [PubMed]
  5. J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62(19), 2205–2208 (1989).
    [CrossRef] [PubMed]
  6. Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65(3), 321–324 (1990).
    [CrossRef] [PubMed]
  7. P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41(5), 2910–2913 (1990).
    [CrossRef] [PubMed]
  8. 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]
  9. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
    [CrossRef]
  10. A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
    [CrossRef]
  11. M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
    [CrossRef]
  12. J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. 82(12), 2594–2597 (1999).
    [CrossRef]
  13. R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93(1), 010503 (2004).
    [CrossRef]
  14. O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
    [CrossRef] [PubMed]
  15. A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19(15), 13770–13778 (2011).
    [CrossRef] [PubMed]
  16. B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13(6), 065029 (2011).
    [CrossRef]
  17. C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109(5), 053602 (2012).
    [CrossRef] [PubMed]
  18. Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83(13), 2556–2559 (1999).
    [CrossRef]
  19. C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97(22), 223601 (2006).
    [CrossRef] [PubMed]
  20. F. Wolfgramm, X. Xing, A. Cerè, A. Predojevi?, A. M. Steinberg, and M. W. Mitchell, “Bright filter-free source of indistinguishable photon pairs,” Opt. Express 16(22), 18145–18151 (2008).
    [CrossRef] [PubMed]
  21. D. Kielpinski, J. F. Corney, and H. M. Wiseman, “Quantum optical waveform conversion,” Phys. Rev. Lett. 106(13), 130501 (2011).
    [CrossRef] [PubMed]
  22. Y. Park, T.-J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
    [CrossRef] [PubMed]
  23. J. L. Walsh, “A Closed Set of Normal Orthogonal Functions,” Am. J. Math. 45(1), 5–24 (1923).
    [CrossRef]
  24. G. Golub and C. VanLoan, Matrix Computations (Johns Hopkins University Press, 3rd ed., 1996).
  25. M. A. Nielsen and I. L. Chuang, Quantum Computation And Quantum Information (Cambridge, 2000).
  26. G. Smith, “Quantum Channel Capacities,” arXiv:1007.2855 (2010).
  27. R. T. Thew, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A 66(1), 012303 (2002).
    [CrossRef]
  28. C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84(23), 5304–5307 (2000).
    [CrossRef] [PubMed]

2012 (1)

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109(5), 053602 (2012).
[CrossRef] [PubMed]

2011 (4)

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19(15), 13770–13778 (2011).
[CrossRef] [PubMed]

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13(6), 065029 (2011).
[CrossRef]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[CrossRef]

D. Kielpinski, J. F. Corney, and H. M. Wiseman, “Quantum optical waveform conversion,” Phys. Rev. Lett. 106(13), 130501 (2011).
[CrossRef] [PubMed]

2010 (1)

T. Vértesi, S. Pironio, and N. Brunner, “Closing the detection loophole in bell experiments using qudits,” Phys. Rev. Lett. 104(6), 060401 (2010).
[CrossRef] [PubMed]

2008 (4)

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[CrossRef]

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

Y. Park, T.-J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16(22), 17817–17825 (2008).
[CrossRef] [PubMed]

F. Wolfgramm, X. Xing, A. Cerè, A. Predojevi?, A. M. Steinberg, and M. W. Mitchell, “Bright filter-free source of indistinguishable photon pairs,” Opt. Express 16(22), 18145–18151 (2008).
[CrossRef] [PubMed]

2007 (2)

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

2006 (1)

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97(22), 223601 (2006).
[CrossRef] [PubMed]

2005 (1)

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95(26), 260501 (2005).
[CrossRef] [PubMed]

2004 (1)

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93(1), 010503 (2004).
[CrossRef]

2002 (1)

R. T. Thew, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A 66(1), 012303 (2002).
[CrossRef]

2001 (1)

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)

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84(23), 5304–5307 (2000).
[CrossRef] [PubMed]

1999 (2)

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. 82(12), 2594–2597 (1999).
[CrossRef]

Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83(13), 2556–2559 (1999).
[CrossRef]

1990 (3)

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65(3), 321–324 (1990).
[CrossRef] [PubMed]

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41(5), 2910–2913 (1990).
[CrossRef] [PubMed]

J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. 64(21), 2495–2498 (1990).
[CrossRef] [PubMed]

1989 (1)

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62(19), 2205–2208 (1989).
[CrossRef] [PubMed]

1923 (1)

J. L. Walsh, “A Closed Set of Normal Orthogonal Functions,” Am. J. Math. 45(1), 5–24 (1923).
[CrossRef]

Acín, A.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93(1), 010503 (2004).
[CrossRef]

Ahn, T.-J.

Andersson, E.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[CrossRef]

Azaña, J.

Barreiro, J. T.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[CrossRef]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95(26), 260501 (2005).
[CrossRef] [PubMed]

Bellini, M.

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109(5), 053602 (2012).
[CrossRef] [PubMed]

Beveratos, A.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
[CrossRef]

Brecht, B.

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13(6), 065029 (2011).
[CrossRef]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19(15), 13770–13778 (2011).
[CrossRef] [PubMed]

Brendel, J.

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. 82(12), 2594–2597 (1999).
[CrossRef]

Brunner, N.

T. Vértesi, S. Pironio, and N. Brunner, “Closing the detection loophole in bell experiments using qudits,” Phys. Rev. Lett. 104(6), 060401 (2010).
[CrossRef] [PubMed]

Buller, G. S.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[CrossRef]

Cassemiro, K. N.

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109(5), 053602 (2012).
[CrossRef] [PubMed]

Cerè, A.

Chiao, R. Y.

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41(5), 2910–2913 (1990).
[CrossRef] [PubMed]

Christ, A.

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13(6), 065029 (2011).
[CrossRef]

Corney, J. F.

D. Kielpinski, J. F. Corney, and H. M. Wiseman, “Quantum optical waveform conversion,” Phys. Rev. Lett. 106(13), 130501 (2011).
[CrossRef] [PubMed]

Dada, A. C.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[CrossRef]

Dai, Y.

Eberly, J. H.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84(23), 5304–5307 (2000).
[CrossRef] [PubMed]

Eckstein, A.

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13(6), 065029 (2011).
[CrossRef]

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19(15), 13770–13778 (2011).
[CrossRef] [PubMed]

Franson, J. D.

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62(19), 2205–2208 (1989).
[CrossRef] [PubMed]

Gisin, N.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
[CrossRef]

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93(1), 010503 (2004).
[CrossRef]

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. 82(12), 2594–2597 (1999).
[CrossRef]

Halder, M.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
[CrossRef]

Hong, C. K.

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41(5), 2910–2913 (1990).
[CrossRef] [PubMed]

Kielpinski, D.

D. Kielpinski, J. F. Corney, and H. M. Wiseman, “Quantum optical waveform conversion,” Phys. Rev. Lett. 106(13), 130501 (2011).
[CrossRef] [PubMed]

Kuklewicz, C. E.

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97(22), 223601 (2006).
[CrossRef] [PubMed]

Kurimura, S.

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

Kuzucu, O.

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

Kwiat, P. G.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[CrossRef]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95(26), 260501 (2005).
[CrossRef] [PubMed]

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41(5), 2910–2913 (1990).
[CrossRef] [PubMed]

Langford, N. K.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95(26), 260501 (2005).
[CrossRef] [PubMed]

Law, C. K.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84(23), 5304–5307 (2000).
[CrossRef] [PubMed]

Leach, J.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[CrossRef]

Lu, Y. J.

Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83(13), 2556–2559 (1999).
[CrossRef]

Mair, A.

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]

Mandel, L.

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65(3), 321–324 (1990).
[CrossRef] [PubMed]

Mitchell, M. W.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

Munro, W. J.

R. T. Thew, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A 66(1), 012303 (2002).
[CrossRef]

Nathel, H.

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41(5), 2910–2913 (1990).
[CrossRef] [PubMed]

Ou, Z. Y.

Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83(13), 2556–2559 (1999).
[CrossRef]

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65(3), 321–324 (1990).
[CrossRef] [PubMed]

Padgett, M. J.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[CrossRef]

Park, Y.

Peters, N. A.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95(26), 260501 (2005).
[CrossRef] [PubMed]

Pironio, S.

T. Vértesi, S. Pironio, and N. Brunner, “Closing the detection loophole in bell experiments using qudits,” Phys. Rev. Lett. 104(6), 060401 (2010).
[CrossRef] [PubMed]

Polycarpou, C.

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109(5), 053602 (2012).
[CrossRef] [PubMed]

Predojevic, A.

Rarity, J. G.

J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. 64(21), 2495–2498 (1990).
[CrossRef] [PubMed]

Scarani, V.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
[CrossRef]

Shapiro, J. H.

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97(22), 223601 (2006).
[CrossRef] [PubMed]

Silberhorn, C.

A. Eckstein, B. Brecht, and C. Silberhorn, “A quantum pulse gate based on spectrally engineered sum frequency generation,” Opt. Express 19(15), 13770–13778 (2011).
[CrossRef] [PubMed]

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13(6), 065029 (2011).
[CrossRef]

Simon, C.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
[CrossRef]

Steinberg, A. M.

Suche, H.

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13(6), 065029 (2011).
[CrossRef]

Tapster, P. R.

J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. 64(21), 2495–2498 (1990).
[CrossRef] [PubMed]

Thew, R. T.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93(1), 010503 (2004).
[CrossRef]

R. T. Thew, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A 66(1), 012303 (2002).
[CrossRef]

Tittel, W.

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. 82(12), 2594–2597 (1999).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

Tovstonog, S.

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

Vareka, W. A.

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41(5), 2910–2913 (1990).
[CrossRef] [PubMed]

Vaziri, A.

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]

Venturi, G.

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109(5), 053602 (2012).
[CrossRef] [PubMed]

Vértesi, T.

T. Vértesi, S. Pironio, and N. Brunner, “Closing the detection loophole in bell experiments using qudits,” Phys. Rev. Lett. 104(6), 060401 (2010).
[CrossRef] [PubMed]

Walmsley, I. A.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84(23), 5304–5307 (2000).
[CrossRef] [PubMed]

Walsh, J. L.

J. L. Walsh, “A Closed Set of Normal Orthogonal Functions,” Am. J. Math. 45(1), 5–24 (1923).
[CrossRef]

Wang, L. J.

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65(3), 321–324 (1990).
[CrossRef] [PubMed]

Wei, T.-C.

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[CrossRef]

Weihs, G.

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]

White, A. G.

R. T. Thew, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A 66(1), 012303 (2002).
[CrossRef]

Wiseman, H. M.

D. Kielpinski, J. F. Corney, and H. M. Wiseman, “Quantum optical waveform conversion,” Phys. Rev. Lett. 106(13), 130501 (2011).
[CrossRef] [PubMed]

Wolfgramm, F.

Wong, F. N. C.

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97(22), 223601 (2006).
[CrossRef] [PubMed]

Xing, X.

Yao, J.

Zavatta, A.

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109(5), 053602 (2012).
[CrossRef] [PubMed]

Zbinden, H.

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
[CrossRef]

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93(1), 010503 (2004).
[CrossRef]

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. 82(12), 2594–2597 (1999).
[CrossRef]

Zeilinger, A.

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]

Zou, X. Y.

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65(3), 321–324 (1990).
[CrossRef] [PubMed]

Am. J. Math. (1)

J. L. Walsh, “A Closed Set of Normal Orthogonal Functions,” Am. J. Math. 45(1), 5–24 (1923).
[CrossRef]

Nat. Phys. (4)

J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7(9), 677–680 (2011).
[CrossRef]

M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3(10), 692–695 (2007).
[CrossRef]

Nature (1)

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]

New J. Phys. (1)

B. Brecht, A. Eckstein, A. Christ, H. Suche, and C. Silberhorn, “From quantum pulse gate to quantum pulse shaper—engineered frequency conversion in nonlinear optical waveguides,” New J. Phys. 13(6), 065029 (2011).
[CrossRef]

Opt. Express (3)

Phys. Rev. A (2)

R. T. Thew, A. G. White, and W. J. Munro, “Qudit quantum-state tomography,” Phys. Rev. A 66(1), 012303 (2002).
[CrossRef]

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41(5), 2910–2913 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett. (13)

D. Kielpinski, J. F. Corney, and H. M. Wiseman, “Quantum optical waveform conversion,” Phys. Rev. Lett. 106(13), 130501 (2011).
[CrossRef] [PubMed]

C. Polycarpou, K. N. Cassemiro, G. Venturi, A. Zavatta, and M. Bellini, “Adaptive detection of arbitrarily shaped ultrashort quantum light states,” Phys. Rev. Lett. 109(5), 053602 (2012).
[CrossRef] [PubMed]

Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83(13), 2556–2559 (1999).
[CrossRef]

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97(22), 223601 (2006).
[CrossRef] [PubMed]

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed Energy-Time Entangled Twin-Photon Source for Quantum Communication,” Phys. Rev. Lett. 82(12), 2594–2597 (1999).
[CrossRef]

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93(1), 010503 (2004).
[CrossRef]

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95(26), 260501 (2005).
[CrossRef] [PubMed]

T. Vértesi, S. Pironio, and N. Brunner, “Closing the detection loophole in bell experiments using qudits,” Phys. Rev. Lett. 104(6), 060401 (2010).
[CrossRef] [PubMed]

J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. 64(21), 2495–2498 (1990).
[CrossRef] [PubMed]

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62(19), 2205–2208 (1989).
[CrossRef] [PubMed]

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Observation of nonlocal interference in separated photon channels,” Phys. Rev. Lett. 65(3), 321–324 (1990).
[CrossRef] [PubMed]

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84(23), 5304–5307 (2000).
[CrossRef] [PubMed]

Other (3)

G. Golub and C. VanLoan, Matrix Computations (Johns Hopkins University Press, 3rd ed., 1996).

M. A. Nielsen and I. L. Chuang, Quantum Computation And Quantum Information (Cambridge, 2000).

G. Smith, “Quantum Channel Capacities,” arXiv:1007.2855 (2010).

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Figures (5)

Fig. 1
Fig. 1

(a) Temporal-pattern multidimensional quantum communication channel. In the transmitter (Tx) a temporal pattern fk(t) is written onto a triggered single photon. In the receiver (Rx) the photon is stored into a loop, where a different pattern is written on each round trip until the photon is transmitted through the filter and detected by a single photon counting module (SPCM), which is time-tagged for coincidences with the triggering SPCM in the Tx. (b) multidimensional time-entanglement state tomography scheme based on temporal pattern writing.

Fig. 2
Fig. 2

(a) examples of phase-flip modulated photon profiles for a 100ns photon wavepacket– much slower than the modulation bandwidth for encoding dimension d = 16 (b) Corresponding power spectra. Calculated ERS dependence on Hilbert space dimension for the phase-flip modulation scheme for different numbers of phase flips (c) for ΔEOMphoton = 100 (d) for ΔEOMphoton = 20.

Fig. 3
Fig. 3

(a) The time dependence of the linear phase modulation profiles assuming a coherence time of 100ns for the photon and 1GHz modulation bandwidth. (b) Corresponding power spectra. (c) Calculated ERS dependence on Hilbert space dimension for the linear phase modulation scheme for different ratios of EOM bandwidth to photon bandwidth, N = ΔEOMphoton. (d) Calculated ERS dependence on (d-1)/N for different N = ΔEOMphoton.

Fig. 4
Fig. 4

(a) Temporal profiles of the d = 4 linear ramp computational basis { | C k } . (b) Temporal profiles of the superposition basis { | S k } . Detection probability matrix p ¯ kj (c) for the computational basis { | C k } and (d) for the superposition basis { | S k } . The filter and EOM parameters are chosen ΔEOMphoton = 10 and Δfilterphoton = 100.

Fig. 5
Fig. 5

(a) Mutual information I(X:Y) versus the ratio of filter bandwidth to photon linewidth, Δfilterphoton. for various values of superposition parameter a, as defined in Eq. (13). The modulation speed of the EOM is chosen so that ΔEOMphoton = 100. The calculation is done for the linear phase ramp scheme, with the encoding dimension d = 16 (for this dimensionality the ideal information is 4 bits/symbol). (b) Dependence of the ERS on the loss level for for different Hilbert space dimensions, d, with dark count rate of 100/s, and 100ns photon coherence time.

Equations (13)

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| ψ k = dω f k ~ ( ω ) a ω |0
p kj = | ψ j | ψ k | 2 = | d ω f ˜ j * ( ω ) dω f ˜ k ( ω )0| a ω a ω |0 | 2 = | dt f j * ( t ) f k ( t ) | 2
p ¯ kj = dω | [ dΩ f j * ~ ( Ω ) f k ~ ( ω+Ω ) ] T ~ (ω) | 2
p ¯ kj = dt | [ dτ f j * ( t ) f k ( t ) ]T(τt) | 2 ,
p ¯ kj T 0 2 τ filter | dτ f j * ( t ) f k ( t ) | 2 = T 0 2 τ filter | Ψ j | Ψ k | 2
ϕ i ( t )= j=1 n π 2 ( W ij +1 )[ Θ( t t j )Θ( t t j+1 ) ],i[ 1,n ]
+ ( Θ( t t j )Θ( t t j+1 ) )|f(t) | 2 dt= 1 n + |f(t) | 2 dt.
ERS= 1 d i=1 d ji d p ¯ ij j=1 d p ¯ ij = 1 d i=1 d ( 1 p ¯ ii j=1 d p ¯ ij ) ,
N= Δ EOM / Δ photon ,
| ψ k = dω f ˜ k ( ω Δ k ) a ω |0
Δ k =k Δ EOM / ( d1 )
| S 1 =0.267| C 1 +0.413| C 2 0.785| C 3 0.376| C 4 | S 2 =0.187| C 1 +0.593| C 2 +0.610| C 3 0.491| C 4 | S 3 =0.936| C 1 0.324| C 2 +0.103| C 3 +0.094| C 4 | S 4 =0.134| C 1 +0.611| C 2 0.006| C 3 +0.780| C 4
|Ψ= 1 a 2 | ω k +a e ib | ω j

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