Abstract

Frequency-bin quantum information encoding offers an intriguing synergy with classical optical networks, with the ability to support many qubits in a single fiber. Yet, coherent quantum frequency operations prove extremely challenging due to the difficulties in mixing frequencies arbitrarily and with low noise. In this paper, we address such challenges and implement distinct quantum gates in parallel on two entangled frequency-bin qubits in the same optical fiber. Our basic quantum operation controls the spectral overlap between adjacent spectral bins, allowing us to observe frequency-bin Hong–Ou–Mandel interference with a visibility of 0.971±0.007. By integrating this tunability with frequency parallelization, we synthesize independent gates on entangled qubits and flip their spectral correlations, allowing us to observe strong violation of the separability bound. Our realization of closed, user-defined gates on frequency-bin qubits in parallel should find application in the development of fiber-compatible quantum information processing and quantum networks.

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

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References

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    [Crossref]
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    [Crossref]
  25. A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284, 3669–3692 (2011).
    [Crossref]
  26. J. M. Lukens and P. Lougovski, “Frequency-encoded photonic qubits for scalable quantum information processing,” Optica 4, 8–16 (2017).
    [Crossref]
  27. 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]
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    [Crossref]
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    [Crossref]
  30. J. S. Bell, “On the Einstein Poldolsky Rosen paradox,” Physics Physique Fizika 1, 195–200 (1964).
    [Crossref]
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  33. We note that, due to low signal-to-noise ratios, the experiment in Ref. [19] required subtraction of accidental coincidences to exceed the classical limit, so we do not include its 84% visibility in the comparison in the main text. Incidentally, if we subtract accidentals from the present results [Fig. 3(b)], the visibility will increase to ∼100%.
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    [Crossref]
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    [Crossref]
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    [Crossref]
  37. R. Blume-Kohout, “Optimal, reliable estimation of quantum states,” New J. Phys. 12, 043034 (2010).
    [Crossref]
  38. B. P. Williams and P. Lougovski, “Quantum state estimation when qubits are lost: a no-data-left-behind approach,” New J. Phys. 19, 043003 (2017).
    [Crossref]

2018 (6)

2017 (7)

J. M. Lukens and P. Lougovski, “Frequency-encoded photonic qubits for scalable quantum information processing,” Optica 4, 8–16 (2017).
[Crossref]

P. J. Coles, M. Berta, M. Tomamichel, and S. Wehner, “Entropic uncertainty relations and their applications,” Rev. Mod. Phys. 89, 015002 (2017).
[Crossref]

J. A. Jaramillo-Villegas, P. Imany, O. D. Odele, D. E. Leaird, Z.-Y. Ou, M. Qi, and A. M. Weiner, “Persistent energy-time entanglement covering multiple resonances of an on-chip biphoton frequency comb,” Optica 4, 655–658 (2017).
[Crossref]

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

L. J. Wright, M. Karpiński, C. Söller, and B. J. Smith, “Spectral shearing of quantum light pulses by electro-optic phase modulation,” Phys. Rev. Lett. 118, 023601 (2017).
[Crossref]

N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Sci. Adv. 3, e1701491 (2017).
[Crossref]

B. P. Williams and P. Lougovski, “Quantum state estimation when qubits are lost: a no-data-left-behind approach,” New J. Phys. 19, 043003 (2017).
[Crossref]

2016 (5)

T. Kobayashi, R. Ikuta, S. Yasui, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Koashi, and N. Imoto, “Frequency-domain Hong-Ou–Mandel interference,” Nat. Photonics 10, 441–444 (2016).
[Crossref]

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interference with single photons,” Phys. Rev. Lett. 117, 223601 (2016).
[Crossref]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

J. M. Donohue, M. Mastrovich, and K. J. Resch, “Spectrally engineering photonic entanglement with a time lens,” Phys. Rev. Lett. 117, 243602 (2016).
[Crossref]

P. Manurkar, N. Jain, M. Silver, Y.-P. Huang, C. Langrock, M. M. Fejer, P. Kumar, and G. S. Kanter, “Multidimensional mode-separable frequency conversion for high-speed quantum communication,” Optica 3, 1300–1307 (2016).
[Crossref]

2015 (3)

Z. Xie, T. Zhong, S. Shrestha, X. Xu, J. Liang, Y.-X. Gong, J. C. Bienfang, A. Restelli, J. H. Shapiro, F. N. C. Wong, and C. W. Wong, “Harnessing high-dimensional hyperentanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
[Crossref]

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: a complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).
[Crossref]

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time-energy entanglement with high-dimensional encoding,” New J. Phys. 17, 022002 (2015).
[Crossref]

2014 (2)

N. Sinclair, E. Saglamyurek, H. Mallahzadeh, J. A. Slater, M. George, R. Ricken, M. P. Hedges, D. Oblak, C. Simon, W. Sohler, and W. Tittel, “Spectral multiplexing for scalable quantum photonics using an atomic frequency comb quantum memory and feed-forward control,” Phys. Rev. Lett. 113, 053603 (2014).
[Crossref]

J. M. Lukens, A. Dezfooliyan, C. Langrock, M. M. Fejer, D. E. Leaird, and A. M. Weiner, “Orthogonal spectral coding of entangled photons,” Phys. Rev. Lett. 112, 133602 (2014).
[Crossref]

2013 (1)

P. C. Humphreys, B. J. Metcalf, J. B. Spring, M. Moore, X.-M. Jin, M. Barbieri, W. S. Kolthammer, and I. A. Walmsley, “Linear optical quantum computing in a single spatial mode,” Phys. Rev. Lett. 111, 150501 (2013).
[Crossref]

2011 (1)

A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284, 3669–3692 (2011).
[Crossref]

2010 (2)

R. Blume-Kohout, “Optimal, reliable estimation of quantum states,” New J. Phys. 12, 043034 (2010).
[Crossref]

M. Raymer, S. van Enk, C. McKinstrie, and H. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
[Crossref]

2007 (1)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[Crossref]

2005 (1)

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

2003 (1)

Y. J. Lu, R. L. Campbell, and Z. Y. Ou, “Mode-locked two-photon states,” Phys. Rev. Lett. 91, 163602 (2003).
[Crossref]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

1992 (1)

J. Huang and P. Kumar, “Observation of quantum frequency conversion,” Phys. Rev. Lett. 68, 2153–2156 (1992).
[Crossref]

1988 (1)

H. Maassen and J. B. M. Uffink, “Generalized entropic uncertainty relations,” Phys. Rev. Lett. 60, 1103–1106 (1988).
[Crossref]

1987 (1)

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]

1964 (1)

J. S. Bell, “On the Einstein Poldolsky Rosen paradox,” Physics Physique Fizika 1, 195–200 (1964).
[Crossref]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Alibart, O.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

Allgaier, M.

V. Ansari, J. M. Donohue, M. Allgaier, L. Sansoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, “Tomography and purification of the temporal-mode structure of quantum light,” Phys. Rev. Lett. 120, 213601 (2018).
[Crossref]

Alshaykh, M. S.

Ansari, V.

V. Ansari, J. M. Donohue, B. Brecht, and C. Silberhorn, “Tailoring nonlinear processes for quantum optics with pulsed temporal-mode encodings,” Optica 5, 534–550 (2018).
[Crossref]

V. Ansari, J. M. Donohue, M. Allgaier, L. Sansoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, “Tomography and purification of the temporal-mode structure of quantum light,” Phys. Rev. Lett. 120, 213601 (2018).
[Crossref]

Azaña, J.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Baldi, P.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
[Crossref]

Barbieri, M.

P. C. Humphreys, B. J. Metcalf, J. B. Spring, M. Moore, X.-M. Jin, M. Barbieri, W. S. Kolthammer, and I. A. Walmsley, “Linear optical quantum computing in a single spatial mode,” Phys. Rev. Lett. 111, 150501 (2013).
[Crossref]

Bell, J. S.

J. S. Bell, “On the Einstein Poldolsky Rosen paradox,” Physics Physique Fizika 1, 195–200 (1964).
[Crossref]

Berta, M.

P. J. Coles, M. Berta, M. Tomamichel, and S. Wehner, “Entropic uncertainty relations and their applications,” Rev. Mod. Phys. 89, 015002 (2017).
[Crossref]

Bienfang, J. C.

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time-energy entanglement with high-dimensional encoding,” New J. Phys. 17, 022002 (2015).
[Crossref]

Z. Xie, T. Zhong, S. Shrestha, X. Xu, J. Liang, Y.-X. Gong, J. C. Bienfang, A. Restelli, J. H. Shapiro, F. N. C. Wong, and C. W. Wong, “Harnessing high-dimensional hyperentanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
[Crossref]

Blume-Kohout, R.

R. Blume-Kohout, “Optimal, reliable estimation of quantum states,” New J. Phys. 12, 043034 (2010).
[Crossref]

Brecht, B.

V. Ansari, J. M. Donohue, B. Brecht, and C. Silberhorn, “Tailoring nonlinear processes for quantum optics with pulsed temporal-mode encodings,” Optica 5, 534–550 (2018).
[Crossref]

V. Ansari, J. M. Donohue, M. Allgaier, L. Sansoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, “Tomography and purification of the temporal-mode structure of quantum light,” Phys. Rev. Lett. 120, 213601 (2018).
[Crossref]

B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, “Photon temporal modes: a complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).
[Crossref]

Bromberg, Y.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Cahall, C.

N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, “Provably secure and high-rate quantum key distribution with time-bin qudits,” Sci. Adv. 3, e1701491 (2017).
[Crossref]

Campbell, R. L.

Y. J. Lu, R. L. Campbell, and Z. Y. Ou, “Mode-locked two-photon states,” Phys. Rev. Lett. 91, 163602 (2003).
[Crossref]

Caspani, L.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Chu, S. T.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Cino, A.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Clemmen, S.

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interference with single photons,” Phys. Rev. Lett. 117, 223601 (2016).
[Crossref]

Coles, P. J.

P. J. Coles, M. Berta, M. Tomamichel, and S. Wehner, “Entropic uncertainty relations and their applications,” Rev. Mod. Phys. 89, 015002 (2017).
[Crossref]

Cortés, L. R.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Dezfooliyan, A.

J. M. Lukens, A. Dezfooliyan, C. Langrock, M. M. Fejer, D. E. Leaird, and A. M. Weiner, “Orthogonal spectral coding of entangled photons,” Phys. Rev. Lett. 112, 133602 (2014).
[Crossref]

Donohue, J. M.

V. Ansari, J. M. Donohue, M. Allgaier, L. Sansoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, “Tomography and purification of the temporal-mode structure of quantum light,” Phys. Rev. Lett. 120, 213601 (2018).
[Crossref]

V. Ansari, J. M. Donohue, B. Brecht, and C. Silberhorn, “Tailoring nonlinear processes for quantum optics with pulsed temporal-mode encodings,” Optica 5, 534–550 (2018).
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T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time-energy entanglement with high-dimensional encoding,” New J. Phys. 17, 022002 (2015).
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Z. Xie, T. Zhong, S. Shrestha, X. Xu, J. Liang, Y.-X. Gong, J. C. Bienfang, A. Restelli, J. H. Shapiro, F. N. C. Wong, and C. W. Wong, “Harnessing high-dimensional hyperentanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
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T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, R. P. Mirin, T. Gerrits, S. W. Nam, F. Marsili, M. D. Shaw, Z. Zhang, L. Wang, D. Englund, G. W. Wornell, J. H. Shapiro, and F. N. C. Wong, “Photon-efficient quantum key distribution using time-energy entanglement with high-dimensional encoding,” New J. Phys. 17, 022002 (2015).
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Nat. Photonics (2)

Z. Xie, T. Zhong, S. Shrestha, X. Xu, J. Liang, Y.-X. Gong, J. C. Bienfang, A. Restelli, J. H. Shapiro, F. N. C. Wong, and C. W. Wong, “Harnessing high-dimensional hyperentanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
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T. Kobayashi, R. Ikuta, S. Yasui, S. Miki, T. Yamashita, H. Terai, T. Yamamoto, M. Koashi, and N. Imoto, “Frequency-domain Hong-Ou–Mandel interference,” Nat. Photonics 10, 441–444 (2016).
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Nature (2)

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
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S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature 437, 116–120 (2005).
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New J. Phys. (3)

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B. P. Williams and P. Lougovski, “Quantum state estimation when qubits are lost: a no-data-left-behind approach,” New J. Phys. 19, 043003 (2017).
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Opt. Commun. (2)

A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284, 3669–3692 (2011).
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M. Raymer, S. van Enk, C. McKinstrie, and H. McGuinness, “Interference of two photons of different color,” Opt. Commun. 283, 747–752 (2010).
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Opt. Express (1)

Opt. Lett. (1)

Optica (5)

Phys. Rev. (1)

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We note that, due to low signal-to-noise ratios, the experiment in Ref. [19] required subtraction of accidental coincidences to exceed the classical limit, so we do not include its 84% visibility in the comparison in the main text. Incidentally, if we subtract accidentals from the present results [Fig. 3(b)], the visibility will increase to ∼100%.

Supplementary Material (1)

NameDescription
» Supplement 1       We provide details on the experimental setup, theoretical predictions, and calculations of the visibility, entanglement witness, and density matrix.

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Figures (5)

Fig. 1.
Fig. 1. High-level vision of quantum frequency processor. Single photons (spheres) populating a comb of frequency bins propagate through a parallelized network of quantum gates (boxes) performing the desired set of operations. Spheres of a specific color trace the probability amplitudes of a single input photon, so that an ideal measurement will register precisely one click for each color. Frequency superpositions are represented by spheres straddling multiple lines, while entangled states are sums of photon products (visualized by clouds containing spheres of the same pair of colors). The specific operations are those we realize experimentally: HOM interference (top) and parallel single-qubit rotations (bottom).
Fig. 2.
Fig. 2. (a) Experimental configuration. (b) Joint frequency spectrum of source, measured with etalon output connected directly to coincidence detection setup. Frequency bins satisfying nA+nB=1 show strong correlations, whereas all other combinations are at the expected accidentals level. Coincidences are counted over 5 s.
Fig. 3.
Fig. 3. (a) Beamsplitter reflectivities R and transmissivities T for all paths between frequency bins 0 and 1, as pulse shaper phase shift is tuned. Markers denote the values measured with a laser probe, while curves give the theory. (b) Measured output coincidence counts between bins 0 and 1, for a two-photon input (no accidentals subtraction). The HOM visibility is 0.971±0.007. (c) Singles counts in bins 0, 1, 1, and 2 for the same input as (b). Here, detector dark counts are subtracted to compare output flux. For (b) and (c), counts are recorded over 180 s, and error bars assume Poissonian statistics.
Fig. 4.
Fig. 4. Coincidences between output frequency bins after the following gates: (a) 1 on both photons, (b) H on photon A, (c) H on photon B, (d) H on both photons. Coincidences are collected over 120 s.
Fig. 5.
Fig. 5. Density matrix retrieved by BME. (a) Real part of average density matrix. (b) Imaginary part. (c) Standard deviations of the real density matrix elements. (d) Standard deviations of the imaginary elements. Shorthand label definitions: 00|1ω4A|1ω4B, 01|1ω4A|1ω5B, 10|1ω3A|1ω4B, 11|1ω3A|1ω5B.

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