Abstract

A fiber-optic-based coupled waveguide transmission medium is proposed to distribute secret keys in a single-photon polarization-based quantum cryptography setup. Polarization maintenance properties and coupling phenomena of the transmission medium are exploited to achieve accuracy and security of the transferred key. Elliptic fibers and fiber couplers are used to prepare the transmitted photons at the sender as well as analyze them at the receiver. The uniqueness of the setup stands on the exclusive use of fiber-optic components, enabling its construction on a single fiber line.

© 2006 Optical Society of America

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References

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  1. C. E. Shannon, "Communication theory of secrecy systems," Bell Syst. Tech. J. 28, 656-715 (1949).
  2. R. Feynman, R. Leighton, and M. Sands, "The polarization states of the photon" in The Feynman Lectures on Physics (Addison-Wesley, 1971), Vol. 3, pp. 11-9-11-12.
  3. J.-P. Goure and I. Verrier, Optical Fibre Devices (Institute of Physics, 2002).
    [CrossRef]
  4. W. Tittel and G. Weihs, "Photonic entanglement for fundamental tests and quantum communication," Quantum Inf. Comput. 1, 3-56 (2001).
  5. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).
    [CrossRef]
  6. S. Tsakiris and N. Uzunoglu, "Electromagnetic analysis of coupling and guiding phenomena in elliptical cross section parallel waveguides with rotated symmetry planes" J. Opt. Soc. Am. A (to be published).
  7. R. F. Harrington, Field Computation by Moment Methods (Macmillan, 1968).
  8. R. B. Dyott, Elliptic Fiber Waveguides (Artech House, 1995).
  9. A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poisat, and P. Granzier, "Single photon quantum cryptography," Phys. Rev. Lett. 89, 187901 (2002).
    [CrossRef] [PubMed]
  10. C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, "Stable solid-state source of single photons," Phys. Rev. Lett. 85, 290-293 (2000).
    [CrossRef] [PubMed]
  11. F. De Martini, G. Di Giuseppe, and M. Marrocco, "Single-mode generation of quantum photon states by excited single molecules in a microcavity trap," Phys. Rev. Lett. 76, 900-903 (1996).
    [CrossRef] [PubMed]

2002 (2)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poisat, and P. Granzier, "Single photon quantum cryptography," Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef] [PubMed]

2001 (1)

W. Tittel and G. Weihs, "Photonic entanglement for fundamental tests and quantum communication," Quantum Inf. Comput. 1, 3-56 (2001).

2000 (1)

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, "Stable solid-state source of single photons," Phys. Rev. Lett. 85, 290-293 (2000).
[CrossRef] [PubMed]

1996 (1)

F. De Martini, G. Di Giuseppe, and M. Marrocco, "Single-mode generation of quantum photon states by excited single molecules in a microcavity trap," Phys. Rev. Lett. 76, 900-903 (1996).
[CrossRef] [PubMed]

1949 (1)

C. E. Shannon, "Communication theory of secrecy systems," Bell Syst. Tech. J. 28, 656-715 (1949).

Beveratos, A.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poisat, and P. Granzier, "Single photon quantum cryptography," Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef] [PubMed]

Brouri, R.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poisat, and P. Granzier, "Single photon quantum cryptography," Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef] [PubMed]

De Martini, F.

F. De Martini, G. Di Giuseppe, and M. Marrocco, "Single-mode generation of quantum photon states by excited single molecules in a microcavity trap," Phys. Rev. Lett. 76, 900-903 (1996).
[CrossRef] [PubMed]

Di Giuseppe, G.

F. De Martini, G. Di Giuseppe, and M. Marrocco, "Single-mode generation of quantum photon states by excited single molecules in a microcavity trap," Phys. Rev. Lett. 76, 900-903 (1996).
[CrossRef] [PubMed]

Dyott, R. B.

R. B. Dyott, Elliptic Fiber Waveguides (Artech House, 1995).

Feynman, R.

R. Feynman, R. Leighton, and M. Sands, "The polarization states of the photon" in The Feynman Lectures on Physics (Addison-Wesley, 1971), Vol. 3, pp. 11-9-11-12.

Gacoin, T.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poisat, and P. Granzier, "Single photon quantum cryptography," Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef] [PubMed]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

Goure, J.-P.

J.-P. Goure and I. Verrier, Optical Fibre Devices (Institute of Physics, 2002).
[CrossRef]

Granzier, P.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poisat, and P. Granzier, "Single photon quantum cryptography," Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef] [PubMed]

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Macmillan, 1968).

Kurtsiefer, C.

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, "Stable solid-state source of single photons," Phys. Rev. Lett. 85, 290-293 (2000).
[CrossRef] [PubMed]

Leighton, R.

R. Feynman, R. Leighton, and M. Sands, "The polarization states of the photon" in The Feynman Lectures on Physics (Addison-Wesley, 1971), Vol. 3, pp. 11-9-11-12.

Marrocco, M.

F. De Martini, G. Di Giuseppe, and M. Marrocco, "Single-mode generation of quantum photon states by excited single molecules in a microcavity trap," Phys. Rev. Lett. 76, 900-903 (1996).
[CrossRef] [PubMed]

Mayer, S.

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, "Stable solid-state source of single photons," Phys. Rev. Lett. 85, 290-293 (2000).
[CrossRef] [PubMed]

Poisat, J.-P.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poisat, and P. Granzier, "Single photon quantum cryptography," Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef] [PubMed]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

Sands, M.

R. Feynman, R. Leighton, and M. Sands, "The polarization states of the photon" in The Feynman Lectures on Physics (Addison-Wesley, 1971), Vol. 3, pp. 11-9-11-12.

Shannon, C. E.

C. E. Shannon, "Communication theory of secrecy systems," Bell Syst. Tech. J. 28, 656-715 (1949).

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

W. Tittel and G. Weihs, "Photonic entanglement for fundamental tests and quantum communication," Quantum Inf. Comput. 1, 3-56 (2001).

Tsakiris, S.

S. Tsakiris and N. Uzunoglu, "Electromagnetic analysis of coupling and guiding phenomena in elliptical cross section parallel waveguides with rotated symmetry planes" J. Opt. Soc. Am. A (to be published).

Uzunoglu, N.

S. Tsakiris and N. Uzunoglu, "Electromagnetic analysis of coupling and guiding phenomena in elliptical cross section parallel waveguides with rotated symmetry planes" J. Opt. Soc. Am. A (to be published).

Verrier, I.

J.-P. Goure and I. Verrier, Optical Fibre Devices (Institute of Physics, 2002).
[CrossRef]

Villing, A.

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poisat, and P. Granzier, "Single photon quantum cryptography," Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef] [PubMed]

Weihs, G.

W. Tittel and G. Weihs, "Photonic entanglement for fundamental tests and quantum communication," Quantum Inf. Comput. 1, 3-56 (2001).

Weinfurter, H.

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, "Stable solid-state source of single photons," Phys. Rev. Lett. 85, 290-293 (2000).
[CrossRef] [PubMed]

Zarda, P.

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, "Stable solid-state source of single photons," Phys. Rev. Lett. 85, 290-293 (2000).
[CrossRef] [PubMed]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

Bell Syst. Tech. J. (1)

C. E. Shannon, "Communication theory of secrecy systems," Bell Syst. Tech. J. 28, 656-715 (1949).

Phys. Rev. Lett. (3)

A. Beveratos, R. Brouri, T. Gacoin, A. Villing, J.-P. Poisat, and P. Granzier, "Single photon quantum cryptography," Phys. Rev. Lett. 89, 187901 (2002).
[CrossRef] [PubMed]

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, "Stable solid-state source of single photons," Phys. Rev. Lett. 85, 290-293 (2000).
[CrossRef] [PubMed]

F. De Martini, G. Di Giuseppe, and M. Marrocco, "Single-mode generation of quantum photon states by excited single molecules in a microcavity trap," Phys. Rev. Lett. 76, 900-903 (1996).
[CrossRef] [PubMed]

Quantum Inf. Comput. (1)

W. Tittel and G. Weihs, "Photonic entanglement for fundamental tests and quantum communication," Quantum Inf. Comput. 1, 3-56 (2001).

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys. 74, 145-195 (2002).
[CrossRef]

Other (5)

S. Tsakiris and N. Uzunoglu, "Electromagnetic analysis of coupling and guiding phenomena in elliptical cross section parallel waveguides with rotated symmetry planes" J. Opt. Soc. Am. A (to be published).

R. F. Harrington, Field Computation by Moment Methods (Macmillan, 1968).

R. B. Dyott, Elliptic Fiber Waveguides (Artech House, 1995).

R. Feynman, R. Leighton, and M. Sands, "The polarization states of the photon" in The Feynman Lectures on Physics (Addison-Wesley, 1971), Vol. 3, pp. 11-9-11-12.

J.-P. Goure and I. Verrier, Optical Fibre Devices (Institute of Physics, 2002).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Transversal cross section of the quantum medium.

Fig. 2
Fig. 2

Field distributions in (a), (c) guide 1 and (b), (d) guide 2 of an elliptic coupler with a 45° angle between symmetry planes for the slow HE11 mode. (a), (b) even slow HE11 mode. (c), (d) odd slow HE11 mode. Distance d / α = 6 between guides is considered.

Fig. 3
Fig. 3

Field distributions in (a), (c) guide 1 and (b), (d) guide 2 of an elliptic coupler with a 45° angle between symmetry planes for the fast HE11 mode. (a), (b) even fast HE11 mode. (c), (d) odd fast HE11 mode. The distance d / α = 6 between guides is considered.

Fig. 4
Fig. 4

Transmitter setup. Arrows depict the possible polarization states of the propagating photons (↑, 0°; →, 90°; ↖, −45°; ↗, +45°).

Fig. 5
Fig. 5

Receiver setup. Arrows depict the possible polarization states of the propagating photons (↑, 0°; →, 90°; ↖, −45°; ↗, +45°).

Tables (3)

Tables Icon

Table 1 Normalized Propagation Constants a

Tables Icon

Table 2 Production of Polarization States at the Transmitter

Tables Icon

Table 3 Decoding of Polarization States at the Receiver

Equations (12)

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E ( r ) = ρ A ( ρ ) exp ( j β z )
E ( r ) = k 0 2 ( n 1 2 - n 0 2 ) V 1 d r G ¯ ( r , r ) E 1 ( r ) + k 0 2 ( n 1 2 - n 0 2 ) V 2 d r G ¯ ( r , r ) E 2 ( r ) ,
E 1 ˙ ( r ) = ϕ k = 0 2 π d ϕ k c 1 ( k ) e j a k ρ e j β z ,
E 2 ˙ ( r ) = ϕ k = 0 2 π d ϕ k c 2 ( k ) e j a k ρ e j β z ,
ϕ k = 0 2 π d ϕ k c j ( k ) e j a k ρ e j β z = i = 1 2 V i d r G ¯ ( r , r ) × ϕ k = 0 2 π d ϕ k c i ( k ) e j a k ρ e j β z k 0 2 × ( n 1 2 - n 0 2 ) ,
E 1 = x A e j β s e z + x B e j β s o z + y Γ e j β f e z + y Δ e j β f o z ,
E 2 = x + y 2 A e j β s e z x + y 2 B e j β s o z + x y 2 Γ e j β f e z x y 2 Δ e j β f o z ,
E 1 = x A e j β s e z + x B e j β s o z ,
E 2 = x + y 2 A e j β s e z x + y 2 B e j β s o z .
E 1 = y Γ e j β f e z + y Δ e j β f o z ,
E 2 = x y 2 Γ e j β f e z x y 2 Δ e j β f o z .
L s = π / 2 β s e β s o ,   L f = π / 2 β f e β f o .

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