Abstract

We study the feasibility of nonlocally compensating for polarization mode dispersion (PMD), when polarization entangled photons are distributed in fiber-optic channels. We quantify the effectiveness of nonlocal compensation while taking into account the possibility that entanglement is generated through the use of a pulsed optical pump signal.

© 2011 OSA

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  1. H. Hubel, M. R. Vanner, T. Lederer, B. Blauensteiner, T. Lorunser, A. Poppe, and A. Zeilinger, “High-fidelity transmission of polarization encoded qubits from an entangled source over 100 km of fiber,” Opt. Express 15, 7853–7862 (2007).
    [CrossRef] [PubMed]
  2. I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002).
    [CrossRef]
  3. M. Brodsky, E. George, C. Antonelli, and M. Shtaif, “Loss of Polarization Entanglement in Optical Fibers due to Polarization Mode Dispersion,” Proc. Opt. Fiber. Comm. Conf. (OFC)San Diego2010, paper PDPA1.
  4. J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000).
    [CrossRef] [PubMed]
  5. M. Brodsky, K. E. George, C. Antonelli, and M. Shtaif, “Loss of polarization entanglement in a fiber-optic system with polarization mode dispersion in one optical path,” Opt. Lett. 36(1), 43–45 (2011).
    [CrossRef] [PubMed]
  6. H. Sunnerud and M. Karlsson “Analytical theory for PMD compensation,” IEEE Photon. Technol. Lett. 12, 50–52 (2000).
    [CrossRef]
  7. J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
    [CrossRef] [PubMed]
  8. J. D. Franson, “Nonclassical nature of dispersion cancellation and nonlocal interferometry,” Phys. Rev. A 80, 031119 (2009).
    [CrossRef]
  9. P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental Verification of Decoherence-Free Subspaces,” Science 290, 498–501 (2000).
    [CrossRef] [PubMed]
  10. J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental Investigation of a Two-Qubit Decoherence-Free Subspace,” Phys. Rev. Lett. 92, 147901 (2004).
    [CrossRef] [PubMed]
  11. W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
    [CrossRef]
  12. X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express 12, 3737–3744 (2004).
    [CrossRef] [PubMed]
  13. S. X. Wang and G. S. Kanter, “Robust Multiwavelength All-Fiber Source of Polarization-Entangled Photons With Built-In Analyzer Alignment Signal,” IEEE J. Sel. Top. Quantum Electron. 15, 1733–1740 (2009).
    [CrossRef]
  14. H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bells inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802 (2004).
    [CrossRef]
  15. M. Brodsky, N. J. Frigo, M. Boroditsky, and M. Tur, “Polarization Mode Dispersion of Installed Fibers,” J. Lightwave Technol. 24, 4584–4599 (2006).
    [CrossRef]
  16. M. Shtaif and A. Mecozzi, “Study of the frequency autocorrelation of the differential group delay in fibers with polarization mode dispersion,” Opt. Lett. 25, 707–709 (2000).
    [CrossRef]
  17. The same expression with small modifications to the waveform part applies to the case where entanglement is generated in a χ3 nonlinear optical medium. A possible phase difference between the two polarization terms, which often follows from the experimental procedure of photon generation [12], is immaterial to our analysis and is therefore omitted.
  18. W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
    [CrossRef]

2011 (1)

2009 (2)

J. D. Franson, “Nonclassical nature of dispersion cancellation and nonlocal interferometry,” Phys. Rev. A 80, 031119 (2009).
[CrossRef]

S. X. Wang and G. S. Kanter, “Robust Multiwavelength All-Fiber Source of Polarization-Entangled Photons With Built-In Analyzer Alignment Signal,” IEEE J. Sel. Top. Quantum Electron. 15, 1733–1740 (2009).
[CrossRef]

2007 (1)

2006 (1)

2004 (3)

H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bells inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802 (2004).
[CrossRef]

X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express 12, 3737–3744 (2004).
[CrossRef] [PubMed]

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental Investigation of a Two-Qubit Decoherence-Free Subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[CrossRef] [PubMed]

2002 (1)

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002).
[CrossRef]

2000 (4)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000).
[CrossRef] [PubMed]

H. Sunnerud and M. Karlsson “Analytical theory for PMD compensation,” IEEE Photon. Technol. Lett. 12, 50–52 (2000).
[CrossRef]

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental Verification of Decoherence-Free Subspaces,” Science 290, 498–501 (2000).
[CrossRef] [PubMed]

M. Shtaif and A. Mecozzi, “Study of the frequency autocorrelation of the differential group delay in fibers with polarization mode dispersion,” Opt. Lett. 25, 707–709 (2000).
[CrossRef]

1998 (1)

W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

1997 (1)

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
[CrossRef]

1992 (1)

J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
[CrossRef] [PubMed]

Altepeter, J. B.

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental Investigation of a Two-Qubit Decoherence-Free Subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[CrossRef] [PubMed]

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental Verification of Decoherence-Free Subspaces,” Science 290, 498–501 (2000).
[CrossRef] [PubMed]

Antonelli, C.

M. Brodsky, K. E. George, C. Antonelli, and M. Shtaif, “Loss of polarization entanglement in a fiber-optic system with polarization mode dispersion in one optical path,” Opt. Lett. 36(1), 43–45 (2011).
[CrossRef] [PubMed]

M. Brodsky, E. George, C. Antonelli, and M. Shtaif, “Loss of Polarization Entanglement in Optical Fibers due to Polarization Mode Dispersion,” Proc. Opt. Fiber. Comm. Conf. (OFC)San Diego2010, paper PDPA1.

Berglund, A. J.

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental Investigation of a Two-Qubit Decoherence-Free Subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[CrossRef] [PubMed]

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental Verification of Decoherence-Free Subspaces,” Science 290, 498–501 (2000).
[CrossRef] [PubMed]

Blauensteiner, B.

Boroditsky, M.

Brodsky, M.

Chen, J.

de Riedmatten, H.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002).
[CrossRef]

Franson, J. D.

J. D. Franson, “Nonclassical nature of dispersion cancellation and nonlocal interferometry,” Phys. Rev. A 80, 031119 (2009).
[CrossRef]

J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
[CrossRef] [PubMed]

Frigo, N. J.

George, E.

M. Brodsky, E. George, C. Antonelli, and M. Shtaif, “Loss of Polarization Entanglement in Optical Fibers due to Polarization Mode Dispersion,” Proc. Opt. Fiber. Comm. Conf. (OFC)San Diego2010, paper PDPA1.

George, K. E.

Gisin, N.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002).
[CrossRef]

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000).
[CrossRef] [PubMed]

Grice, W. P.

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
[CrossRef]

Hadley, P. G.

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental Investigation of a Two-Qubit Decoherence-Free Subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[CrossRef] [PubMed]

Hubel, H.

Inoue, K.

H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bells inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802 (2004).
[CrossRef]

Kanter, G. S.

S. X. Wang and G. S. Kanter, “Robust Multiwavelength All-Fiber Source of Polarization-Entangled Photons With Built-In Analyzer Alignment Signal,” IEEE J. Sel. Top. Quantum Electron. 15, 1733–1740 (2009).
[CrossRef]

Karlsson, M.

H. Sunnerud and M. Karlsson “Analytical theory for PMD compensation,” IEEE Photon. Technol. Lett. 12, 50–52 (2000).
[CrossRef]

Kogelnik, H.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000).
[CrossRef] [PubMed]

Kumar, P.

Kwiat, P. G.

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental Investigation of a Two-Qubit Decoherence-Free Subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[CrossRef] [PubMed]

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental Verification of Decoherence-Free Subspaces,” Science 290, 498–501 (2000).
[CrossRef] [PubMed]

Lederer, T.

Li, X.

Lorunser, T.

Marcikic, I.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002).
[CrossRef]

Mecozzi, A.

Poppe, A.

Scarani, V.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002).
[CrossRef]

Sharping, J.

Shtaif, M.

Sunnerud, H.

H. Sunnerud and M. Karlsson “Analytical theory for PMD compensation,” IEEE Photon. Technol. Lett. 12, 50–52 (2000).
[CrossRef]

Takesue, H.

H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bells inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802 (2004).
[CrossRef]

Tittel, W.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002).
[CrossRef]

Tur, M.

Vanner, M. R.

Voss, P.

Walmsley, I. A.

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
[CrossRef]

Wang, S. X.

S. X. Wang and G. S. Kanter, “Robust Multiwavelength All-Fiber Source of Polarization-Entangled Photons With Built-In Analyzer Alignment Signal,” IEEE J. Sel. Top. Quantum Electron. 15, 1733–1740 (2009).
[CrossRef]

Wendelken, S. M.

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental Investigation of a Two-Qubit Decoherence-Free Subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[CrossRef] [PubMed]

White, A. G.

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental Verification of Decoherence-Free Subspaces,” Science 290, 498–501 (2000).
[CrossRef] [PubMed]

Wootters, W. K.

W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

Zbinden, H.

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002).
[CrossRef]

Zeilinger, A.

IEEE J. Sel. Top. Quantum Electron. (1)

S. X. Wang and G. S. Kanter, “Robust Multiwavelength All-Fiber Source of Polarization-Entangled Photons With Built-In Analyzer Alignment Signal,” IEEE J. Sel. Top. Quantum Electron. 15, 1733–1740 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. Sunnerud and M. Karlsson “Analytical theory for PMD compensation,” IEEE Photon. Technol. Lett. 12, 50–52 (2000).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (5)

H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bells inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802 (2004).
[CrossRef]

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
[CrossRef]

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66, 062308 (2002).
[CrossRef]

J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
[CrossRef] [PubMed]

J. D. Franson, “Nonclassical nature of dispersion cancellation and nonlocal interferometry,” Phys. Rev. A 80, 031119 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental Investigation of a Two-Qubit Decoherence-Free Subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[CrossRef] [PubMed]

W. K. Wootters, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: Polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97, 4541–4550 (2000).
[CrossRef] [PubMed]

Science (1)

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental Verification of Decoherence-Free Subspaces,” Science 290, 498–501 (2000).
[CrossRef] [PubMed]

Other (2)

M. Brodsky, E. George, C. Antonelli, and M. Shtaif, “Loss of Polarization Entanglement in Optical Fibers due to Polarization Mode Dispersion,” Proc. Opt. Fiber. Comm. Conf. (OFC)San Diego2010, paper PDPA1.

The same expression with small modifications to the waveform part applies to the case where entanglement is generated in a χ3 nonlinear optical medium. A possible phase difference between the two polarization terms, which often follows from the experimental procedure of photon generation [12], is immaterial to our analysis and is therefore omitted.

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Figures (2)

Fig. 1
Fig. 1

Nonlocal PMD compensation set-up. The compensator in Bob’s path contains two stages. The first compensates Bob’s PMD, the second compensates for Alice’s PMD.

Fig. 2
Fig. 2

(a) The concurrence as a function of the the DGD of Bob’s compensator normalized by the DGD in Alice’s optical path. The red and blue curves correspond to pump bandwidths of B p = 0.1 τ a 1 and B p = τ a 1, respectively. (b) The best achievable concurrence after PMD compensation, as a function of the pump bandwidth Bp normalized by τ a 1, where the green and black curves correspond to photon bandwidths of B = 2 τ a 1 and B = τ a 1 respectively. The solid curves are drawn for typical telecom filter-shapes (super-Gaussian), whereas the dashed curves show the analytical expressions in the Gaussian case.

Equations (6)

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| ψ = 1 2 π d ω a d ω b H a * ( ω a ) H b * ( ω b ) E ˜ p ( ω a + ω b ) | ω a , ω b 1 2 [ | u _ a , u _ b + | u _ a , u _ b ] .
1 2 π d ω a d ω b H a * ( ω a ) H b * ( ω b ) E ˜ p ( ω a + ω b ) | ω a , ω b = d t a d t b g ( t a , t b ) | t a , t b
| ψ out = 1 2 | g ( t a τ a / 2 , t b τ b / 2 ) | s _ a , s _ b + 1 2 | g ( t a + τ a / 2 , t b + τ b / 2 ) | s _ a , s _ b ,
C ( τ a , τ b ) = | d t a d t b g ( t a , t b ) g * ( t a + τ a , t b + τ b ) | ,
C ( τ a , τ b ) = exp [ 1 2 ( τ a τ b ) 2 B a 2 B b 2 B p 2 + B a 2 + B b 2 ] exp [ 1 2 B p 2 ( B a 2 τ a 2 + B b 2 τ b 2 ) B p 2 + B a 2 + B b 2 ] .
C opt = exp [ 1 2 τ a 2 B p 2 + B a 2 ] ,

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