Abstract

We demonstrate three and four input multiports in a three dimensional glass platform, fabricated using the femtosecond laser direct-write technique. Hong-Ou-Mandel (HOM) interference is observed and a full quantum characterization is performed, obtaining two photon correlation matrices for all combinations of input and output ports. For the 3-port case, the quantum visibilities are accurately predicted solely from measurement of the classical coupling ratios.

© 2012 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
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  5. T. Brougham, V. Košták, I. Jex, E. Andersson, and T. Kiss, “Entanglement preparation using symmetric multiports,” Eur. Phys. J. D61, 231–236 (2011).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  26. R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A81, 023834 (2010).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  30. I. J. Myung, “Tutorial on maximum likelihood estimation,” J. Math. Psychol.47, 90–100 (2003).
    [CrossRef]
  31. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
    [CrossRef] [PubMed]
  32. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
    [CrossRef]

2012

S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, and D. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser and Photon. Rev.6, 115–143 (2012).
[CrossRef]

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6, 45–49 (2012).
[CrossRef]

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett.108, 053601 (2012).
[CrossRef] [PubMed]

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, and Y. S. Kivshar, “Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides,” Phys. Rev. Lett.108, 023601 (2012).
[CrossRef] [PubMed]

A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Photonics8, 285–291 (2012).

M. Delanty, S. Rebić, and J. Twamley, “Novel collective effects in integrated photonics,” Eur. Phys. J. D66, 1–7 (2012).
[CrossRef]

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett.108, 010502 (2012).
[CrossRef] [PubMed]

2011

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

T. Brougham, V. Košták, I. Jex, E. Andersson, and T. Kiss, “Entanglement preparation using symmetric multiports,” Eur. Phys. J. D61, 231–236 (2011).
[CrossRef]

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

2010

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-ii ppln waveguide emitting at a telecom wavelength,” New J. Phys12, 103005 (2010).
[CrossRef]

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A81, 023834 (2010).
[CrossRef]

2009

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express17, 12546–12554 (2009).
[CrossRef] [PubMed]

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett.102, 253904 (2009).
[CrossRef] [PubMed]

2008

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett.100, 170506 (2008).
[CrossRef] [PubMed]

2007

2005

2003

I. J. Myung, “Tutorial on maximum likelihood estimation,” J. Math. Psychol.47, 90–100 (2003).
[CrossRef]

G. J. Pryde and A. G. White, “Creation of maximally entangled photon-number states using optical fiber multiports,” Phys. Rev. A68, 052315 (2003).
[CrossRef]

2001

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
[CrossRef]

1997

M. Żukowski, A. Zeilinger, and M. A. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A55, 2564–2579 (1997).
[CrossRef]

1996

G. Weihs, M. Reck, H. Weinfurter, and A. Zeilinger, “Two-photon interference in optical fiber multiports,” Phys. Rev. A54, 893–897 (1996).
[CrossRef] [PubMed]

1995

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Nonclassical statistics at multiport beam-splitters,” Appl. Phys. B, Lasers O.60, 111–117 (1995).

1994

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett.73, 58–61 (1994).
[CrossRef] [PubMed]

1987

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

1972

Alibart, O.

S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, and D. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser and Photon. Rev.6, 115–143 (2012).
[CrossRef]

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-ii ppln waveguide emitting at a telecom wavelength,” New J. Phys12, 103005 (2010).
[CrossRef]

Ams, M.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express17, 12546–12554 (2009).
[CrossRef] [PubMed]

Andersson, E.

T. Brougham, V. Košták, I. Jex, E. Andersson, and T. Kiss, “Entanglement preparation using symmetric multiports,” Eur. Phys. J. D61, 231–236 (2011).
[CrossRef]

Arai, A.

Aspuru-Guzik, A.

A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Photonics8, 285–291 (2012).

Bernstein, H. J.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett.73, 58–61 (1994).
[CrossRef] [PubMed]

Bertani, P.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett.73, 58–61 (1994).
[CrossRef] [PubMed]

Biggerstaff, D. N.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

Bonneau, D.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett.108, 053601 (2012).
[CrossRef] [PubMed]

Bovatsek, J.

Bromberg, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett.102, 253904 (2009).
[CrossRef] [PubMed]

Broome, M. A.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

Brougham, T.

T. Brougham, V. Košták, I. Jex, E. Andersson, and T. Kiss, “Entanglement preparation using symmetric multiports,” Eur. Phys. J. D61, 231–236 (2011).
[CrossRef]

Calkins, B.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Calvez, S.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

Christodoulides, D. N.

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Quantum state transformations by multiport array beam splitters,” in “CLEO: QELS-Fundamental Science,” (Optical Society of America, 2012), p. QTh1E.2.

Crespi, A.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett.108, 010502 (2012).
[CrossRef] [PubMed]

Cryan, M. J.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

Dawson, M. D.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

De Micheli, M.

S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, and D. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser and Photon. Rev.6, 115–143 (2012).
[CrossRef]

Dekker, P.

Delanty, M.

M. Delanty, S. Rebić, and J. Twamley, “Novel collective effects in integrated photonics,” Eur. Phys. J. D66, 1–7 (2012).
[CrossRef]

Dorenbos, S. N.

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett.108, 053601 (2012).
[CrossRef] [PubMed]

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Dreisow, F.

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A81, 023834 (2010).
[CrossRef]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express15, 1579–1587 (2007).
[CrossRef] [PubMed]

Eaton, S.

Engin, E.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

Ezaki, M.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Fedrizzi, A.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

Fox, A. E.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Gates, J. C.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

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T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Goggin, M. E.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

Gu, E.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

Hadfield, R. H.

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett.108, 053601 (2012).
[CrossRef] [PubMed]

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Heinrich, M.

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A81, 023834 (2010).
[CrossRef]

Herman, P.

Herrmann, H.

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-ii ppln waveguide emitting at a telecom wavelength,” New J. Phys12, 103005 (2010).
[CrossRef]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

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M. Żukowski, A. Zeilinger, and M. A. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A55, 2564–2579 (1997).
[CrossRef]

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D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Ismail, N.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

Issautier, A.

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-ii ppln waveguide emitting at a telecom wavelength,” New J. Phys12, 103005 (2010).
[CrossRef]

James, D. F. V.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
[CrossRef]

Jex, I.

T. Brougham, V. Košták, I. Jex, E. Andersson, and T. Kiss, “Entanglement preparation using symmetric multiports,” Eur. Phys. J. D61, 231–236 (2011).
[CrossRef]

Jiang, P.

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett.108, 053601 (2012).
[CrossRef] [PubMed]

Kaiser, F.

S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, and D. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser and Photon. Rev.6, 115–143 (2012).
[CrossRef]

Keil, R.

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A81, 023834 (2010).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Quantum state transformations by multiport array beam splitters,” in “CLEO: QELS-Fundamental Science,” (Optical Society of America, 2012), p. QTh1E.2.

Kiss, T.

T. Brougham, V. Košták, I. Jex, E. Andersson, and T. Kiss, “Entanglement preparation using symmetric multiports,” Eur. Phys. J. D61, 231–236 (2011).
[CrossRef]

Kivshar, Y. S.

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, and Y. S. Kivshar, “Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides,” Phys. Rev. Lett.108, 023601 (2012).
[CrossRef] [PubMed]

Košták, V.

T. Brougham, V. Košták, I. Jex, E. Andersson, and T. Kiss, “Entanglement preparation using symmetric multiports,” Eur. Phys. J. D61, 231–236 (2011).
[CrossRef]

Kwiat, P. G.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
[CrossRef]

Lahini, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett.102, 253904 (2009).
[CrossRef] [PubMed]

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett.100, 170506 (2008).
[CrossRef] [PubMed]

Laing, A.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6, 45–49 (2012).
[CrossRef]

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

Langford, N. K.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Linares, A. L.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Linjordet, T.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

Lita, A. E.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Lobino, M.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6, 45–49 (2012).
[CrossRef]

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett.108, 053601 (2012).
[CrossRef] [PubMed]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

Marshall, G. D.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express17, 12546–12554 (2009).
[CrossRef] [PubMed]

Martin, A.

S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, and D. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser and Photon. Rev.6, 115–143 (2012).
[CrossRef]

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-ii ppln waveguide emitting at a telecom wavelength,” New J. Phys12, 103005 (2010).
[CrossRef]

Mataloni, P.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett.108, 010502 (2012).
[CrossRef] [PubMed]

Matsuda, N.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

Matthews, J. C. F.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6, 45–49 (2012).
[CrossRef]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express17, 12546–12554 (2009).
[CrossRef] [PubMed]

Mattle, K.

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Nonclassical statistics at multiport beam-splitters,” Appl. Phys. B, Lasers O.60, 111–117 (1995).

McKnight, L.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

Metcalf, B. J.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Michler, M.

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Nonclassical statistics at multiport beam-splitters,” Appl. Phys. B, Lasers O.60, 111–117 (1995).

Mirin, R. P.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Morandotti, R.

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett.102, 253904 (2009).
[CrossRef] [PubMed]

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett.100, 170506 (2008).
[CrossRef] [PubMed]

Moya-Cessa, H.

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Quantum state transformations by multiport array beam splitters,” in “CLEO: QELS-Fundamental Science,” (Optical Society of America, 2012), p. QTh1E.2.

Munro, W. J.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
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I. J. Myung, “Tutorial on maximum likelihood estimation,” J. Math. Psychol.47, 90–100 (2003).
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Nam, S. W.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Natarajan, C. M.

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett.108, 053601 (2012).
[CrossRef] [PubMed]

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Neshev, D. N.

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, and Y. S. Kivshar, “Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides,” Phys. Rev. Lett.108, 023601 (2012).
[CrossRef] [PubMed]

Nolte, S.

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A81, 023834 (2010).
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A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express15, 1579–1587 (2007).
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O’Brien, J. L.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6, 45–49 (2012).
[CrossRef]

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett.108, 053601 (2012).
[CrossRef] [PubMed]

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express17, 12546–12554 (2009).
[CrossRef] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

OBrien, J. L.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

Ohira, K.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

Osellame, R.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett.108, 010502 (2012).
[CrossRef] [PubMed]

Ostrowsky, D.

S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, and D. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser and Photon. Rev.6, 115–143 (2012).
[CrossRef]

Ostrowsky, D. B.

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-ii ppln waveguide emitting at a telecom wavelength,” New J. Phys12, 103005 (2010).
[CrossRef]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59, 2044–2046 (1987).
[CrossRef] [PubMed]

Owens, J. O.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

Perets, H. B.

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett.100, 170506 (2008).
[CrossRef] [PubMed]

Perez-Leija, A.

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Quantum state transformations by multiport array beam splitters,” in “CLEO: QELS-Fundamental Science,” (Optical Society of America, 2012), p. QTh1E.2.

Pertsch, T.

Peruzzo, A.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6, 45–49 (2012).
[CrossRef]

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

Politi, A.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6, 45–49 (2012).
[CrossRef]

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express17, 12546–12554 (2009).
[CrossRef] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

Poulios, K.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

Pozzi, F.

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett.100, 170506 (2008).
[CrossRef] [PubMed]

Pryde, G. J.

G. J. Pryde and A. G. White, “Creation of maximally entangled photon-number states using optical fiber multiports,” Phys. Rev. A68, 052315 (2003).
[CrossRef]

Ramponi, R.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett.108, 010502 (2012).
[CrossRef] [PubMed]

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

Rebic, S.

M. Delanty, S. Rebić, and J. Twamley, “Novel collective effects in integrated photonics,” Eur. Phys. J. D66, 1–7 (2012).
[CrossRef]

Reck, M.

G. Weihs, M. Reck, H. Weinfurter, and A. Zeilinger, “Two-photon interference in optical fiber multiports,” Phys. Rev. A54, 893–897 (1996).
[CrossRef] [PubMed]

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett.73, 58–61 (1994).
[CrossRef] [PubMed]

Rudolph, T.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

Sansoni, L.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett.108, 010502 (2012).
[CrossRef] [PubMed]

Sciarrino, F.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett.108, 010502 (2012).
[CrossRef] [PubMed]

Shadbolt, P. J.

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6, 45–49 (2012).
[CrossRef]

Shah, L.

Silberberg, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, “Quantum and classical correlations in waveguide lattices,” Phys. Rev. Lett.102, 253904 (2009).
[CrossRef] [PubMed]

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett.100, 170506 (2008).
[CrossRef] [PubMed]

Smith, P. G. R.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

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Sohler, W.

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-ii ppln waveguide emitting at a telecom wavelength,” New J. Phys12, 103005 (2010).
[CrossRef]

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A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, and Y. S. Kivshar, “Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides,” Phys. Rev. Lett.108, 023601 (2012).
[CrossRef] [PubMed]

Sorel, M.

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett.100, 170506 (2008).
[CrossRef] [PubMed]

Spring, J. B.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Sukhorukov, A. A.

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, and Y. S. Kivshar, “Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides,” Phys. Rev. Lett.108, 023601 (2012).
[CrossRef] [PubMed]

Suzuki, N.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

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R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A81, 023834 (2010).
[CrossRef]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express15, 1579–1587 (2007).
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A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Quantum state transformations by multiport array beam splitters,” in “CLEO: QELS-Fundamental Science,” (Optical Society of America, 2012), p. QTh1E.2.

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D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett.108, 053601 (2012).
[CrossRef] [PubMed]

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S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, and D. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser and Photon. Rev.6, 115–143 (2012).
[CrossRef]

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-ii ppln waveguide emitting at a telecom wavelength,” New J. Phys12, 103005 (2010).
[CrossRef]

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T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

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D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett.108, 053601 (2012).
[CrossRef] [PubMed]

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6, 45–49 (2012).
[CrossRef]

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

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T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Tünnermann, A.

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A81, 023834 (2010).
[CrossRef]

A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, “Control of directional evanescent coupling in fs laser written waveguides,” Opt. Express15, 1579–1587 (2007).
[CrossRef] [PubMed]

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M. Delanty, S. Rebić, and J. Twamley, “Novel collective effects in integrated photonics,” Eur. Phys. J. D66, 1–7 (2012).
[CrossRef]

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

Vallone, G.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Two-particle bosonic-fermionic quantum walk via integrated photonics,” Phys. Rev. Lett.108, 010502 (2012).
[CrossRef] [PubMed]

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P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6, 45–49 (2012).
[CrossRef]

Walmsley, I. A.

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

Walther, P.

A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Photonics8, 285–291 (2012).

Watson, I. M.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

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G. Weihs, M. Reck, H. Weinfurter, and A. Zeilinger, “Two-photon interference in optical fiber multiports,” Phys. Rev. A54, 893–897 (1996).
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Weinfurter, H.

G. Weihs, M. Reck, H. Weinfurter, and A. Zeilinger, “Two-photon interference in optical fiber multiports,” Phys. Rev. A54, 893–897 (1996).
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K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Nonclassical statistics at multiport beam-splitters,” Appl. Phys. B, Lasers O.60, 111–117 (1995).

White, A. G.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
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G. J. Pryde and A. G. White, “Creation of maximally entangled photon-number states using optical fiber multiports,” Phys. Rev. A68, 052315 (2003).
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D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
[CrossRef]

Withford, M. J.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express17, 12546–12554 (2009).
[CrossRef] [PubMed]

Wörhoff, K.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

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D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

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Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science320, 646–649 (2008).
[CrossRef] [PubMed]

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M. Żukowski, A. Zeilinger, and M. A. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A55, 2564–2579 (1997).
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G. Weihs, M. Reck, H. Weinfurter, and A. Zeilinger, “Two-photon interference in optical fiber multiports,” Phys. Rev. A54, 893–897 (1996).
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K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Nonclassical statistics at multiport beam-splitters,” Appl. Phys. B, Lasers O.60, 111–117 (1995).

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett.73, 58–61 (1994).
[CrossRef] [PubMed]

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Zhang, Y.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

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A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010).
[CrossRef] [PubMed]

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M. Żukowski, A. Zeilinger, and M. A. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A55, 2564–2579 (1997).
[CrossRef]

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Nonclassical statistics at multiport beam-splitters,” Appl. Phys. B, Lasers O.60, 111–117 (1995).

Zwiller, V.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
[CrossRef]

D. Bonneau, M. Lobino, P. Jiang, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, M. G. Thompson, and J. L. O’Brien, “Fast path and polarization manipulation of telecom wavelength single photons in lithium niobate waveguide devices,” Phys. Rev. Lett.108, 053601 (2012).
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App. Phys. Lett.

Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” App. Phys. Lett.99, 161119 (2011).
[CrossRef]

Appl. Phys. B, Lasers O.

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Żukowski, “Nonclassical statistics at multiport beam-splitters,” Appl. Phys. B, Lasers O.60, 111–117 (1995).

Eur. Phys. J. D

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S. Tanzilli, A. Martin, F. Kaiser, M. De Micheli, O. Alibart, and D. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser and Photon. Rev.6, 115–143 (2012).
[CrossRef]

Nat. Commun.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun.2, 224 (2011).
[CrossRef] [PubMed]

Nat. Photonics

A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Photonics8, 285–291 (2012).

P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit,” Nat. Photonics6, 45–49 (2012).
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New J. Phys

A. Martin, A. Issautier, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “A polarization entangled photon-pair source based on a type-ii ppln waveguide emitting at a telecom wavelength,” New J. Phys12, 103005 (2010).
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New J. Phys.

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys.13, 075003 (2011).
[CrossRef]

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys.14, 045003 (2012).
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Opt. Express

Phys. Rev. A

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, “Photon correlations in two-dimensional waveguide arrays and their classical estimate,” Phys. Rev. A81, 023834 (2010).
[CrossRef]

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001).
[CrossRef]

T. Gerrits, N. Thomas-Peter, J. C. Gates, A. E. Lita, B. J. Metcalf, B. Calkins, N. A. Tomlin, A. E. Fox, A. L. Linares, J. B. Spring, N. K. Langford, R. P. Mirin, P. G. R. Smith, I. A. Walmsley, and S. W. Nam, “On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing,” Phys. Rev. A84, 060301 (2011).
[CrossRef]

G. Weihs, M. Reck, H. Weinfurter, and A. Zeilinger, “Two-photon interference in optical fiber multiports,” Phys. Rev. A54, 893–897 (1996).
[CrossRef] [PubMed]

G. J. Pryde and A. G. White, “Creation of maximally entangled photon-number states using optical fiber multiports,” Phys. Rev. A68, 052315 (2003).
[CrossRef]

M. Żukowski, A. Zeilinger, and M. A. Horne, “Realizable higher-dimensional two-particle entanglements via multiport beam splitters,” Phys. Rev. A55, 2564–2579 (1997).
[CrossRef]

Phys. Rev. Lett.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett.73, 58–61 (1994).
[CrossRef] [PubMed]

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, “Realization of quantum walks with negligible decoherence in waveguide lattices,” Phys. Rev. Lett.100, 170506 (2008).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1:
Fig. 1:

(a) Idealised coupling region of a tritter device. Writing considerations induce an effective isosceles geometry with two coupling strengths g(z) and G(z). (b) A schematic of a 3D implementation of a tritter, where three waveguides taper from a planar arrangement to a triangular interaction region, shown in the inset microscope image, and taper back to a planar array and (c) the layout of the four directional couplers and the waveguide avoided crossing in the 4-port device

Fig. 2:
Fig. 2:

Tritter visibilities as a function of effective coupling, ḡL. We assume uniform coupling over an interaction region of length L, g(0 ≤ zL)L/νp =ḡ and G(0 ≤ zL)L/νp = Ḡ with zero coupling elsewhere. a) symmetric coupling region (Ḡ = ḡ). b) Isosceles coupling region (Ḡ = 0.6234ḡ). Vertical line corresponds to the fit to our experimental tritter with ḡL ≈ 0.81νp.

Fig. 3:
Fig. 3:

Tritter HOM dips for (a) input ports 1 and 2, (b) for input ports 2 and 3 (c) for input ports 1 and 3. (d) Comparison of measured tritter visibilities (error bars) and theoretical predictions (columns) from the simple tritter model in section 4.

Fig. 4:
Fig. 4:

Four-port HOM dips for (a) input ports 1 and 2, (b) for input ports 1 and 3 (c) for input ports 1 and 4 (c) for input ports 2 and 3 (d) for input ports 2 and 4 (e) for input ports 3 and 4. (f) Experimental four-port visibility matrix determined from the HOM dips. (g) Comparison of measured four port visibilities (error bars) and theoretical predictions (columns) from the four-port model. Note the slight offset in the minimum values in each graph is due to photon collection arm realignments required after each measurement resulting from thermal drift.

Equations (14)

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[ b ^ i b ^ j b ^ N ] = [ U 1 , 1 U 1 , 2 U 1 , N U 2 , 1 U 2 , 2 U 2 , N U N , 1 U N , 2 U N , N ] [ a ^ i a ^ j a ^ N ] .
H ^ = h ¯ v p n , m = 1 3 C n , m a ^ n a ^ m ,
C = [ β g G g β g G g β ] .
b ^ = U a ^ ,
U ^ = B ^ 2 , 4 ( η ) B ^ 1 , 3 ( η ) P ^ 2 ( ϕ ) P ^ 3 ( ϕ ) B ^ 3 , 4 ( η ) B ^ 1 , 2 ( η ) ,
[ b ^ i b ^ j ] = B ^ i , j ( η ) [ a ^ i a ^ j ] = [ η i 1 η i 1 η η ] [ a ^ i a ^ j ] ,
U = ( η i e i ϕ ( 1 η ) η i ( 1 η ) η e i ϕ ( η 1 ) i ( 1 η ) η e i ϕ η η 1 i e i ϕ ( 1 η ) η i e i ϕ ( 1 η ) η η 1 e i ϕ η i ( 1 η ) η e i ϕ ( η 1 ) i ( 1 η ) η i e i ϕ ( 1 η ) η η ) .
N j k = ε j in ε k out M | U j , k | 2 ,
F j , r k , s N j k N r s N r k N j s = | U j , k | 2 | U r , s | 2 | U r , k | 2 | U j , s | 2 ,
| U tritter | 2 = ( 0.37 0.41 0.23 0.41 0.19 0.41 0.23 0.41 0.37 ) .
| U 4 port | 2 = ( 0.14 0.23 0.23 0.39 0.23 0.14 0.39 0.23 0.23 0.39 0.14 0.23 0.39 0.23 0.23 0.14 ) .
V i , j k , l = C i , j k , l Q i , j k , l C i , j k , l ,
Q i , j k , l = 1 1 + δ i , j | U i , k U j , l + U i , l U j , k | 2
C i , j k , l = | U i , k U j , l | 2 + | U i , l U j , k | 2 ,

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