Abstract

We employed an electrically driven polarization controller to implement anisotropic depolarizing quantum channels for the polarization state of single photons. The channels were characterized by means of ancilla-assisted quantum process tomography using polarization-entangled photons generated in the process of spontaneous parametric downconversion. The demonstrated depolarization method offers good repeatability, low cost, and compatibility with fiber-optic setups. It does not perturb the modal structure of single photons, and therefore can be used to verify experimentally protocols for managing decoherence effects based on multiphoton interference.

© 2008 Optical Society of America

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  1. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722-725 (1996).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. 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]
  5. M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett. 91, 187903 (2003).
    [CrossRef] [PubMed]
  6. Q. Zhang, J. Yin, T.-Y. Chen, S. Lu, J. Zhang, X.-Q. Li, T. Yang, X.-B. Wang, and J.-W. Pan, “Experimental fault-tolerant quantum cryptography in a decoherence-free subspace,” Phys. Rev. A 73, 020301 (2006).
    [CrossRef]
  7. M. Ricci, F. De Martini, N. J. Cerf, R. Filip, J. Fiurásek, and C. Macchiavello, “Experimental purification of single qubits,” Phys. Rev. Lett. 93, 170501 (2004).
    [CrossRef] [PubMed]
  8. T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of quantum error correction using linear optics,” Phys. Rev. A 71, 052332 (2005).
    [CrossRef]
  9. D. Leung, L. Vandersypen, X. Zhou, M. Sherwood, C. Yannoni, M. Kubinec, and I. Chuang, “Experimental realization of a two-bit phase damping quantum code,” Phys. Rev. A 60, 1924-1943 (1999).
    [CrossRef]
  10. J. W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067-1070 (2001).
    [CrossRef] [PubMed]
  11. G. Puentes, D. Voigt, A. Aiello, and J. P. Woerdman, “Tunable spatial decoherers for polarization-entangled photons,” Opt. Lett. 31, 2057-2059 (2006).
    [CrossRef] [PubMed]
  12. A. B. U'Ren, K. Banaszek, and I. A. Walmsley, “Photon engineering for quantum information processing,” Quantum Inf. Comput. 3, 480-502 (2003).
  13. T. S. Humble and W. P. Grice, “Spectral effects in quantum teleportation,” Phys. Rev. A 75, 022307 (2007).
    [CrossRef]
  14. J.-P. Goure and I. Verrier, Optical Fibre Devices (Institute of Physics, 2002), pp. 152-158.
  15. J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. O'Brien, M. A. Nielsen, and A. G. White, “Ancilla-assisted quantum process tomography,” Phys. Rev. Lett. 90, 193601 (2003).
    [CrossRef] [PubMed]
  16. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons”, Phys. Rev. A 60, R773-R776 (1999)
    [CrossRef]
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    [CrossRef]
  18. L. Yan, Q. Yu, and A. E. Winner, “Uniformly distributed states of polarization on the Poincaré sphere using an improved polarization scrambling scheme,” Opt. Commun. 249, 43-50 (2005).
    [CrossRef]
  19. K. Perlicki, “Investigation of the state of polarization distribution generated by polarization scramblers on the Poincaré sphere,” Opt. Commun. 252, 43-50 (2005).
    [CrossRef]
  20. Y. K. Lizé, R. Gomma, R. Kashyap, L. Palmer, and A. E. Willner, “Fast all-fiber polarization scrambling using re-entrant Lefevre controller,” Opt. Commun. 279, 50-52 (2007).
    [CrossRef]
  21. C. King and M. B. Ruskai, “Minimal entropy of states emerging from noisy quantum channels,” IEEE Trans. Inf. Theory 47, 192-209 (2001).
    [CrossRef]
  22. M. Horodecki and R. Horodecki, “Information-theoretic aspects of inseparability of mixed states,” Phys. Rev. A 54, 1838-1843 (1996).
    [CrossRef] [PubMed]
  23. M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, “Generation and characterization of Werner states and maximally entangled mixed states by a universal source of entanglement,” Phys. Rev. Lett. 92, 177901 (2004).
    [CrossRef] [PubMed]
  24. K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (1999).
    [CrossRef]
  25. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
    [CrossRef]

2007 (2)

T. S. Humble and W. P. Grice, “Spectral effects in quantum teleportation,” Phys. Rev. A 75, 022307 (2007).
[CrossRef]

Y. K. Lizé, R. Gomma, R. Kashyap, L. Palmer, and A. E. Willner, “Fast all-fiber polarization scrambling using re-entrant Lefevre controller,” Opt. Commun. 279, 50-52 (2007).
[CrossRef]

2006 (2)

G. Puentes, D. Voigt, A. Aiello, and J. P. Woerdman, “Tunable spatial decoherers for polarization-entangled photons,” Opt. Lett. 31, 2057-2059 (2006).
[CrossRef] [PubMed]

Q. Zhang, J. Yin, T.-Y. Chen, S. Lu, J. Zhang, X.-Q. Li, T. Yang, X.-B. Wang, and J.-W. Pan, “Experimental fault-tolerant quantum cryptography in a decoherence-free subspace,” Phys. Rev. A 73, 020301 (2006).
[CrossRef]

2005 (3)

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of quantum error correction using linear optics,” Phys. Rev. A 71, 052332 (2005).
[CrossRef]

L. Yan, Q. Yu, and A. E. Winner, “Uniformly distributed states of polarization on the Poincaré sphere using an improved polarization scrambling scheme,” Opt. Commun. 249, 43-50 (2005).
[CrossRef]

K. Perlicki, “Investigation of the state of polarization distribution generated by polarization scramblers on the Poincaré sphere,” Opt. Commun. 252, 43-50 (2005).
[CrossRef]

2004 (3)

M. Ricci, F. De Martini, N. J. Cerf, R. Filip, J. Fiurásek, and C. Macchiavello, “Experimental purification of single qubits,” Phys. Rev. Lett. 93, 170501 (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]

M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, “Generation and characterization of Werner states and maximally entangled mixed states by a universal source of entanglement,” Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef] [PubMed]

2003 (3)

M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett. 91, 187903 (2003).
[CrossRef] [PubMed]

A. B. U'Ren, K. Banaszek, and I. A. Walmsley, “Photon engineering for quantum information processing,” Quantum Inf. Comput. 3, 480-502 (2003).

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. O'Brien, M. A. Nielsen, and A. G. White, “Ancilla-assisted quantum process tomography,” Phys. Rev. Lett. 90, 193601 (2003).
[CrossRef] [PubMed]

2001 (3)

C. King and M. B. Ruskai, “Minimal entropy of states emerging from noisy quantum channels,” IEEE Trans. Inf. Theory 47, 192-209 (2001).
[CrossRef]

J. W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067-1070 (2001).
[CrossRef] [PubMed]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

2000 (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]

1999 (3)

D. Leung, L. Vandersypen, X. Zhou, M. Sherwood, C. Yannoni, M. Kubinec, and I. Chuang, “Experimental realization of a two-bit phase damping quantum code,” Phys. Rev. A 60, 1924-1943 (1999).
[CrossRef]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons”, Phys. Rev. A 60, R773-R776 (1999)
[CrossRef]

K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (1999).
[CrossRef]

1996 (2)

M. Horodecki and R. Horodecki, “Information-theoretic aspects of inseparability of mixed states,” Phys. Rev. A 54, 1838-1843 (1996).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722-725 (1996).
[CrossRef] [PubMed]

1972 (1)

A. Jamiolkowski, “Linear transformations which preserve trace and positive semidefiniteness of operators,” Rep. Math. Phys. 3, 275-278 (1972).
[CrossRef]

IEEE Trans. Inf. Theory (1)

C. King and M. B. Ruskai, “Minimal entropy of states emerging from noisy quantum channels,” IEEE Trans. Inf. Theory 47, 192-209 (2001).
[CrossRef]

Nature (1)

J. W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067-1070 (2001).
[CrossRef] [PubMed]

Opt. Commun. (3)

L. Yan, Q. Yu, and A. E. Winner, “Uniformly distributed states of polarization on the Poincaré sphere using an improved polarization scrambling scheme,” Opt. Commun. 249, 43-50 (2005).
[CrossRef]

K. Perlicki, “Investigation of the state of polarization distribution generated by polarization scramblers on the Poincaré sphere,” Opt. Commun. 252, 43-50 (2005).
[CrossRef]

Y. K. Lizé, R. Gomma, R. Kashyap, L. Palmer, and A. E. Willner, “Fast all-fiber polarization scrambling using re-entrant Lefevre controller,” Opt. Commun. 279, 50-52 (2007).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (8)

T. S. Humble and W. P. Grice, “Spectral effects in quantum teleportation,” Phys. Rev. A 75, 022307 (2007).
[CrossRef]

P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons”, Phys. Rev. A 60, R773-R776 (1999)
[CrossRef]

Q. Zhang, J. Yin, T.-Y. Chen, S. Lu, J. Zhang, X.-Q. Li, T. Yang, X.-B. Wang, and J.-W. Pan, “Experimental fault-tolerant quantum cryptography in a decoherence-free subspace,” Phys. Rev. A 73, 020301 (2006).
[CrossRef]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of quantum error correction using linear optics,” Phys. Rev. A 71, 052332 (2005).
[CrossRef]

D. Leung, L. Vandersypen, X. Zhou, M. Sherwood, C. Yannoni, M. Kubinec, and I. Chuang, “Experimental realization of a two-bit phase damping quantum code,” Phys. Rev. A 60, 1924-1943 (1999).
[CrossRef]

M. Horodecki and R. Horodecki, “Information-theoretic aspects of inseparability of mixed states,” Phys. Rev. A 54, 1838-1843 (1996).
[CrossRef] [PubMed]

K. Banaszek, G. M. D'Ariano, M. G. A. Paris, and M. F. Sacchi, “Maximum-likelihood estimation of the density matrix,” Phys. Rev. A 61, 010304 (1999).
[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, “Generation and characterization of Werner states and maximally entangled mixed states by a universal source of entanglement,” Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef] [PubMed]

M. Ricci, F. De Martini, N. J. Cerf, R. Filip, J. Fiurásek, and C. Macchiavello, “Experimental purification of single qubits,” Phys. Rev. Lett. 93, 170501 (2004).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722-725 (1996).
[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]

M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett. 91, 187903 (2003).
[CrossRef] [PubMed]

J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. O'Brien, M. A. Nielsen, and A. G. White, “Ancilla-assisted quantum process tomography,” Phys. Rev. Lett. 90, 193601 (2003).
[CrossRef] [PubMed]

Quantum Inf. Comput. (1)

A. B. U'Ren, K. Banaszek, and I. A. Walmsley, “Photon engineering for quantum information processing,” Quantum Inf. Comput. 3, 480-502 (2003).

Rep. Math. Phys. (1)

A. Jamiolkowski, “Linear transformations which preserve trace and positive semidefiniteness of operators,” Rep. Math. Phys. 3, 275-278 (1972).
[CrossRef]

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)

J.-P. Goure and I. Verrier, Optical Fibre Devices (Institute of Physics, 2002), pp. 152-158.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge U. Press, 2002), pp. 425-499.

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Figures (6)

Fig. 1
Fig. 1

Tetrahedron of singular values for unital quantum channels that results from the physical condition of complete positivity. Dots and squares represent channels implemented and characterized experimentally by means of ancilla-assisted quantum process tomography, which is discussed in detail in Section 4. (a)–(d) refer to channels depicted in Fig. 3.

Fig. 2
Fig. 2

Experimental setup. BC, Babinet compensator; BBO, a pair of beta-barium borate crystals; IF, interference filter; F, red filter; MPC, manual fiber polarization controller; EPC, electrically driven fiber polarization controller; PBS, polarizing beam splitter; D1, D2, single-photon detectors.

Fig. 3
Fig. 3

Absolute values of density matrix elements (left) and ellipsoids representing the transformed Bloch sphere (right) measured by ancilla-assisted quantum process tomography for quantum channels obtained by switching between the identity and a selected 180 ° rotation; (a) the input density matrix and the initial Bloch sphere, with selected parallels and meridians marked for reference; (b)–(d) quantum channels obtained by changing the duty cycle of the voltage driving the controller. Note that the points representing the poles of the original sphere do not coincide with the principal axes of the ellipsoids, marked with straight thick black lines.

Fig. 4
Fig. 4

Graph of the singular values for channels of the form ( 1 p ) I + p R as a function of the duty cycle p. Each experimentally characterized channel is represented as a triplet of a square, a circle, and a triangle. The solid lines depict values predicted directly from the value of the duty cycle as ( 1 , 1 2 p , 1 2 p ) .

Fig. 5
Fig. 5

Absolute values of density matrix elements (left) and ellipsoids (right), representing the transformed Bloch sphere shown in Fig. 3a, measured by ancilla-assisted quantum process tomography for quantum channels obtained by switching between the identity and two 180 ° rotations with approximately orthogonal axes. Straight thick black lines mark the orientation of the shortest principal axis of an ellipsoid.

Fig. 6
Fig. 6

Orthogonal projection of triplets of singular values for experimentally implemented channels of the form ( 1 p ) I + p ( R 1 + R 2 ) 2 onto the tetrahedron face. The solid line is the least-square fit to the experimental points, compared to the median marked with a dashed line. The points labeled (a) and (b) correspond to channels depicted in Fig. 5. The singular values are given explicitly in the upper left corner of the plot.

Equations (4)

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r Λ r + a ,
D x ± D y 1 ± D z ,
D = p 0 I + p x R x + p y R y + p z R z ,
Φ Φ = 1 4 ( 1 ̂ 1 ̂ i , j = x , y , z T i j σ ̂ i σ ̂ j ) ,

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