Abstract

We present the experimental implementation and theoretical model of a controllable dephasing quantum channel using photonic systems. The channel is implemented by coupling the polarization and the spatial distribution of light that play, in the perspective of open quantum systems, the role of quantum system and environment, respectively. The capability of controlling our channel allows us to visualize its effects in a quantum system. Different from standard dephasing channels, our channel presents an exotic behavior in the sense that the evolution of a state, from a pure to a mixed state, shows an oscillatory behavior if tracked in the Bloch sphere. Additionally, we report the evolution of the purity and perform a quantum process tomography to obtain the χ matrix associated to our channel.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University, 2011), 10th ed.
  2. M. Ricci, F. D. Martini, N. J. Cerf, R. Filip, J. Fiurášek, and C. Macchiavello, “Experimental purification of single qubits,” Phys. Rev. Lett. 93, 170501 (2004).
    [Crossref] [PubMed]
  3. J.-C. Lee, Y.-C. Jeong, Y.-S. Kim, and Y.-H. Kim, “Experimental demonstration of decoherence suppression via quantum measurement reversal,” Opt. Express 19, 16309–16316 (2011).
    [Crossref] [PubMed]
  4. A. Shaham and H. S. Eisenberg, “Realizing controllable depolarization in photonic quantum-information channels,” Phys. Rev. A 83, 022303 (2011).
    [Crossref]
  5. A. Shaham and H. S. Eisenberg, “Realizing a variable isotropic depolarizer,” Opt. Lett. 37, 2643–2645 (2012).
    [Crossref] [PubMed]
  6. Y.-C. Jeong, J.-C. Lee, and Y.-H. Kim, “Experimental implementation of a fully controllable depolarizing quantum operation,” Phys. Rev. A 87, 014301 (2013).
    [Crossref]
  7. K. A. G. Fisher, R. Prevedel, R. Kaltenbaek, and K. J. Resch, “Optimal linear optical implementation of a single-qubit damping channel,” New Journal of Physics 14, 033016 (2012).
    [Crossref]
  8. A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
    [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. G. B. Lemos, J. O. de Almeida, S. P. Walborn, P. H. S. Ribeiro, and M. Hor-Meyll, “Characterization of a spatial light modulator as a polarization quantum channel,” Phys. Rev. A 89, 042119 (2014).
    [Crossref]
  11. J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
    [Crossref] [PubMed]
  12. G. Colangelo, F. M. Ciurana, L. C. Bianchet, R. J. Sewell, and M. W. Mitchell, “Simultaneous tracking of spin angle and amplitude beyond classical limits,” Nature 543, 525–528 (2017).
    [Crossref] [PubMed]
  13. I. L. Chuang and M. A. Nielsen, “Prescription for experimental determination of the dynamics of a quantum black box,” Journal of Modern Optics 44, 2455–2467 (1997).
    [Crossref]
  14. J. Fiurášek and Z. c. v. Hradil, “Maximum-likelihood estimation of quantum processes,” Phys. Rev. A 63, 020101 (2001).
    [Crossref]
  15. L. J. Salazar-Serrano, A. Valencia, and J. P. Torres, “Tunable beam displacer,” Review of Scientific Instruments 86, 033109 (2015).
    [Crossref] [PubMed]
  16. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
    [Crossref]
  17. B. Saleh and M. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 2013).

2017 (1)

G. Colangelo, F. M. Ciurana, L. C. Bianchet, R. J. Sewell, and M. W. Mitchell, “Simultaneous tracking of spin angle and amplitude beyond classical limits,” Nature 543, 525–528 (2017).
[Crossref] [PubMed]

2015 (1)

L. J. Salazar-Serrano, A. Valencia, and J. P. Torres, “Tunable beam displacer,” Review of Scientific Instruments 86, 033109 (2015).
[Crossref] [PubMed]

2014 (1)

G. B. Lemos, J. O. de Almeida, S. P. Walborn, P. H. S. Ribeiro, and M. Hor-Meyll, “Characterization of a spatial light modulator as a polarization quantum channel,” Phys. Rev. A 89, 042119 (2014).
[Crossref]

2013 (2)

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

Y.-C. Jeong, J.-C. Lee, and Y.-H. Kim, “Experimental implementation of a fully controllable depolarizing quantum operation,” Phys. Rev. A 87, 014301 (2013).
[Crossref]

2012 (2)

K. A. G. Fisher, R. Prevedel, R. Kaltenbaek, and K. J. Resch, “Optimal linear optical implementation of a single-qubit damping channel,” New Journal of Physics 14, 033016 (2012).
[Crossref]

A. Shaham and H. S. Eisenberg, “Realizing a variable isotropic depolarizer,” Opt. Lett. 37, 2643–2645 (2012).
[Crossref] [PubMed]

2011 (2)

J.-C. Lee, Y.-C. Jeong, Y.-S. Kim, and Y.-H. Kim, “Experimental demonstration of decoherence suppression via quantum measurement reversal,” Opt. Express 19, 16309–16316 (2011).
[Crossref] [PubMed]

A. Shaham and H. S. Eisenberg, “Realizing controllable depolarization in photonic quantum-information channels,” Phys. Rev. A 83, 022303 (2011).
[Crossref]

2008 (1)

A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
[Crossref]

2004 (1)

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

2001 (2)

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

J. Fiurášek and Z. c. v. Hradil, “Maximum-likelihood estimation of quantum processes,” Phys. Rev. A 63, 020101 (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]

1997 (1)

I. L. Chuang and M. A. Nielsen, “Prescription for experimental determination of the dynamics of a quantum black box,” Journal of Modern Optics 44, 2455–2467 (1997).
[Crossref]

Almeida, M. P.

A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
[Crossref]

Altepeter, J. B.

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]

Bartlett, S. D.

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

Beil, J.

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

Berglund, A. J.

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]

Bianchet, L. C.

G. Colangelo, F. M. Ciurana, L. C. Bianchet, R. J. Sewell, and M. W. Mitchell, “Simultaneous tracking of spin angle and amplitude beyond classical limits,” Nature 543, 525–528 (2017).
[Crossref] [PubMed]

Cerf, N. J.

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

Chuang, I. L.

I. L. Chuang and M. A. Nielsen, “Prescription for experimental determination of the dynamics of a quantum black box,” Journal of Modern Optics 44, 2455–2467 (1997).
[Crossref]

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University, 2011), 10th ed.

Ciurana, F. M.

G. Colangelo, F. M. Ciurana, L. C. Bianchet, R. J. Sewell, and M. W. Mitchell, “Simultaneous tracking of spin angle and amplitude beyond classical limits,” Nature 543, 525–528 (2017).
[Crossref] [PubMed]

Colangelo, G.

G. Colangelo, F. M. Ciurana, L. C. Bianchet, R. J. Sewell, and M. W. Mitchell, “Simultaneous tracking of spin angle and amplitude beyond classical limits,” Nature 543, 525–528 (2017).
[Crossref] [PubMed]

Davidovich, L.

A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
[Crossref]

de Almeida, J. O.

G. B. Lemos, J. O. de Almeida, S. P. Walborn, P. H. S. Ribeiro, and M. Hor-Meyll, “Characterization of a spatial light modulator as a polarization quantum channel,” Phys. Rev. A 89, 042119 (2014).
[Crossref]

de Melo, F.

A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
[Crossref]

DiVincenzo, D. P.

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

Doherty, A. C.

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

Eisenberg, H. S.

A. Shaham and H. S. Eisenberg, “Realizing a variable isotropic depolarizer,” Opt. Lett. 37, 2643–2645 (2012).
[Crossref] [PubMed]

A. Shaham and H. S. Eisenberg, “Realizing controllable depolarization in photonic quantum-information channels,” Phys. Rev. A 83, 022303 (2011).
[Crossref]

Filip, R.

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

Fisher, K. A. G.

K. A. G. Fisher, R. Prevedel, R. Kaltenbaek, and K. J. Resch, “Optimal linear optical implementation of a single-qubit damping channel,” New Journal of Physics 14, 033016 (2012).
[Crossref]

Fiurášek, J.

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

J. Fiurášek and Z. c. v. Hradil, “Maximum-likelihood estimation of quantum processes,” Phys. Rev. A 63, 020101 (2001).
[Crossref]

Gossard, A. C.

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

Hor-Meyll, M.

G. B. Lemos, J. O. de Almeida, S. P. Walborn, P. H. S. Ribeiro, and M. Hor-Meyll, “Characterization of a spatial light modulator as a polarization quantum channel,” Phys. Rev. A 89, 042119 (2014).
[Crossref]

A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
[Crossref]

Hradil, Z. c. v.

J. Fiurášek and Z. c. v. Hradil, “Maximum-likelihood estimation of quantum processes,” Phys. Rev. A 63, 020101 (2001).
[Crossref]

James, D. F. V.

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

Jeong, Y.-C.

Y.-C. Jeong, J.-C. Lee, and Y.-H. Kim, “Experimental implementation of a fully controllable depolarizing quantum operation,” Phys. Rev. A 87, 014301 (2013).
[Crossref]

J.-C. Lee, Y.-C. Jeong, Y.-S. Kim, and Y.-H. Kim, “Experimental demonstration of decoherence suppression via quantum measurement reversal,” Opt. Express 19, 16309–16316 (2011).
[Crossref] [PubMed]

Kaltenbaek, R.

K. A. G. Fisher, R. Prevedel, R. Kaltenbaek, and K. J. Resch, “Optimal linear optical implementation of a single-qubit damping channel,” New Journal of Physics 14, 033016 (2012).
[Crossref]

Kim, Y.-H.

Y.-C. Jeong, J.-C. Lee, and Y.-H. Kim, “Experimental implementation of a fully controllable depolarizing quantum operation,” Phys. Rev. A 87, 014301 (2013).
[Crossref]

J.-C. Lee, Y.-C. Jeong, Y.-S. Kim, and Y.-H. Kim, “Experimental demonstration of decoherence suppression via quantum measurement reversal,” Opt. Express 19, 16309–16316 (2011).
[Crossref] [PubMed]

Kim, Y.-S.

Kwiat, P. G.

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

Lee, J.-C.

Y.-C. Jeong, J.-C. Lee, and Y.-H. Kim, “Experimental implementation of a fully controllable depolarizing quantum operation,” Phys. Rev. A 87, 014301 (2013).
[Crossref]

J.-C. Lee, Y.-C. Jeong, Y.-S. Kim, and Y.-H. Kim, “Experimental demonstration of decoherence suppression via quantum measurement reversal,” Opt. Express 19, 16309–16316 (2011).
[Crossref] [PubMed]

Lemos, G. B.

G. B. Lemos, J. O. de Almeida, S. P. Walborn, P. H. S. Ribeiro, and M. Hor-Meyll, “Characterization of a spatial light modulator as a polarization quantum channel,” Phys. Rev. A 89, 042119 (2014).
[Crossref]

Lu, H.

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

Macchiavello, C.

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

Marcus, C. M.

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

Martini, F. D.

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

Medford, J.

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

Mitchell, M. W.

G. Colangelo, F. M. Ciurana, L. C. Bianchet, R. J. Sewell, and M. W. Mitchell, “Simultaneous tracking of spin angle and amplitude beyond classical limits,” Nature 543, 525–528 (2017).
[Crossref] [PubMed]

Munro, W. J.

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

Nielsen, M. A.

I. L. Chuang and M. A. Nielsen, “Prescription for experimental determination of the dynamics of a quantum black box,” Journal of Modern Optics 44, 2455–2467 (1997).
[Crossref]

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University, 2011), 10th ed.

Prevedel, R.

K. A. G. Fisher, R. Prevedel, R. Kaltenbaek, and K. J. Resch, “Optimal linear optical implementation of a single-qubit damping channel,” New Journal of Physics 14, 033016 (2012).
[Crossref]

Rashba, E. I.

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

Resch, K. J.

K. A. G. Fisher, R. Prevedel, R. Kaltenbaek, and K. J. Resch, “Optimal linear optical implementation of a single-qubit damping channel,” New Journal of Physics 14, 033016 (2012).
[Crossref]

Ribeiro, P. H. S.

G. B. Lemos, J. O. de Almeida, S. P. Walborn, P. H. S. Ribeiro, and M. Hor-Meyll, “Characterization of a spatial light modulator as a polarization quantum channel,” Phys. Rev. A 89, 042119 (2014).
[Crossref]

Ricci, M.

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

Salazar-Serrano, L. J.

L. J. Salazar-Serrano, A. Valencia, and J. P. Torres, “Tunable beam displacer,” Review of Scientific Instruments 86, 033109 (2015).
[Crossref] [PubMed]

Saleh, B.

B. Saleh and M. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 2013).

Salles, A.

A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
[Crossref]

Sewell, R. J.

G. Colangelo, F. M. Ciurana, L. C. Bianchet, R. J. Sewell, and M. W. Mitchell, “Simultaneous tracking of spin angle and amplitude beyond classical limits,” Nature 543, 525–528 (2017).
[Crossref] [PubMed]

Shaham, A.

A. Shaham and H. S. Eisenberg, “Realizing a variable isotropic depolarizer,” Opt. Lett. 37, 2643–2645 (2012).
[Crossref] [PubMed]

A. Shaham and H. S. Eisenberg, “Realizing controllable depolarization in photonic quantum-information channels,” Phys. Rev. A 83, 022303 (2011).
[Crossref]

Souto Ribeiro, P. H.

A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
[Crossref]

Taylor, J. M.

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

Teich, M.

B. Saleh and M. Teich, Fundamentals of Photonics, Wiley Series in Pure and Applied Optics (Wiley, 2013).

Torres, J. P.

L. J. Salazar-Serrano, A. Valencia, and J. P. Torres, “Tunable beam displacer,” Review of Scientific Instruments 86, 033109 (2015).
[Crossref] [PubMed]

Valencia, A.

L. J. Salazar-Serrano, A. Valencia, and J. P. Torres, “Tunable beam displacer,” Review of Scientific Instruments 86, 033109 (2015).
[Crossref] [PubMed]

Walborn, S. P.

G. B. Lemos, J. O. de Almeida, S. P. Walborn, P. H. S. Ribeiro, and M. Hor-Meyll, “Characterization of a spatial light modulator as a polarization quantum channel,” Phys. Rev. A 89, 042119 (2014).
[Crossref]

A. Salles, F. de Melo, M. P. Almeida, M. Hor-Meyll, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment,” Phys. Rev. A 78, 022322 (2008).
[Crossref]

White, A. G.

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

Journal of Modern Optics (1)

I. L. Chuang and M. A. Nielsen, “Prescription for experimental determination of the dynamics of a quantum black box,” Journal of Modern Optics 44, 2455–2467 (1997).
[Crossref]

Nature (1)

G. Colangelo, F. M. Ciurana, L. C. Bianchet, R. J. Sewell, and M. W. Mitchell, “Simultaneous tracking of spin angle and amplitude beyond classical limits,” Nature 543, 525–528 (2017).
[Crossref] [PubMed]

Nature Nanotechnology (1)

J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, “Self-consistent measurement and state tomography of an exchange-only spin qubit,” Nature Nanotechnology 8, 654–659 (2013).
[Crossref] [PubMed]

New Journal of Physics (1)

K. A. G. Fisher, R. Prevedel, R. Kaltenbaek, and K. J. Resch, “Optimal linear optical implementation of a single-qubit damping channel,” New Journal of Physics 14, 033016 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (6)

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

A. Shaham and H. S. Eisenberg, “Realizing controllable depolarization in photonic quantum-information channels,” Phys. Rev. A 83, 022303 (2011).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 (a) Model of an open quantum system. (b) An initial state passes through a quantum channel in which the original beam is separated into two parallel-propagating beams with orthogonal polarizations. The separation between the output beam centroids is 2dc and occurs only in the y-direction.
Fig. 2
Fig. 2 (a) It shows, in the Bloch sphere, the predicted effect of our channel on various input pure states. The dark regions represent the output polarization states. The spheres correspond to different settings of the parameter dc. (b) It shows the theoretical evolution of the purity for five different input polarization states (Table 1) as the value of dc varies. (c) It shows the evolution of an input left circular polarization state with the parameter dc.
Fig. 3
Fig. 3 Experimental setup composed of four steps. The first step is the preparation of a Gaussian spatial mode. The second step is the preparation of the polarization state. The third step is the experimental implementation of our dephasing channel. Finally, the fourth step is the polarization analyzer.
Fig. 4
Fig. 4 Bloch sphere representation of the output polarization states (red dots) measured for the five initial input states defined in Table 1. The dark region is the same as the one reported in the theoretical section, Fig. 2(a).
Fig. 5
Fig. 5 The points are the experimental results for the purity as a function of the parameter dc. The solid lines correspond to the theoretical prediction for the purity. Each graph shows the behavior of the initial input state defined in Table 1.
Fig. 6
Fig. 6 In the Bloch sphere representation, the path followed by a state is tracked when the parameter dc is evolved. The dots are the experimental data and the solid lines are the theoretical model. The big blue stars are the initial input states defined in Table 1. Graphs (a)–(c) shown the exotic spiral that the states follow. The graphs (d)–(e) show that horizontal and vertical input states do not change.
Fig. 7
Fig. 7 The real parts of the experimental and the theoretical χ matrix are shown. (a) χ matrix for dc = 0. (b) χ matrix for dc = 1.44 mm. The vanishing imaginary parts of χ are not shown.

Tables (1)

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Table 1 Initial polarization states

Equations (13)

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| φ = α | H + β | V ,
| ξ = d q f ( q ) | q ,
| Ψ in = | φ | ξ = α d q f ( q ) | H , q + β d q f ( q ) | V , q .
U ^ ( d c ) | H , q y = e i d c q y | H , q y U ^ ( d c ) | V , q y = e i ( d c q y + φ ) | V , q y ,
ρ ^ out pol = Tr env { U ^ ( d c ) | Ψ in Ψ | in U ^ ( d c ) } ,
f ( q y ) = N e w y 2 ( q y q 0 y ) 2 4 ,
ρ ^ out pol = ( | α | 2 α β * e 2 d c 2 w y 2 e i ( 2 d c q 0 y + φ ) α * β e 2 d c 2 w y 2 e i ( 2 d c q 0 y + φ ) | β | 2 ) .
S 0 = | α | 2 + | β | 2 ,
S 1 = | α | 2 | β | 2 ,
S 2 ( d c ) = 2 | α | | β * | e 2 d c 2 w y 2 cos ( 2 q 0 y d c + φ + Φ ) ,
S 3 ( d c ) = 2 | α | | β * | e 2 d c 2 w y 2 sin ( 2 q 0 y d c + φ + Φ ) ,
P out ( d c ) = 1 2 ( 1 + ( | α | 2 | β | 2 ) 2 + 4 | α β * | 2 e 4 d c 2 w y 2 ) .
ρ ^ out pol = i , j χ i j σ ^ i ρ ^ in pol σ ^ j ,

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