Abstract

In the past few years, physicists and engineers have demonstrated the possibility of utilizing multiple degrees of freedom of the photon to perform information processing tasks for a wide variety of applications. Furthermore, complex states of light offer the possibility of encoding and processing many bits of information in a single photon. However, the challenges involved in the process of extracting large amounts of information, encoded in photonic states, impose practical limitations to realistic quantum technologies. Here, we demonstrate characterization of quantum correlated photon pairs in the spatial and spectral degrees of freedom. Our technique utilizes a series of random projective measurements in the spatial basis that do not perturb the spectral properties of the photon. The sparsity in the spatial properties of downconverted photons allows us to exploit the potential of compressive sensing to reduce the number of measurements to reconstruct spatial and spectral properties of correlated photon pairs at telecom wavelength. We demonstrate characterization of a photonic state with 12×109 dimensions using only 20% of the measurements with respect to the conventional raster scan technique. Our characterization technique opens the possibility of increasing and exploiting the complexity and dimensionality of quantum protocols that utilize multiple degrees of freedom of light with high efficiency.

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

Full Article  |  PDF Article
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2018 (1)

S. H. Knarr, D. J. Lum, J. Schneeloch, and J. C. Howell, “Compressive direct imaging of a billion-dimensional optical phase space,” Phys. Rev. A 98, 023854 (2018).
[Crossref]

2017 (4)

M. Kues, C. Reimer, P. Roztocki, L. Romero-Cortes, S. Sciara, B. Wetzel, L. Caspani, J. Azana, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

L. Martin, D. Mardani, H. E. Kondakci, A. N. Vamivakas, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

Z. Yang, O. S. Magana-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. Hashemi Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light: Sci. Appl. 6, e17013 (2017).
[Crossref]

D. Oren, M. Mutzafi, Y. C. Eldar, and M. Segev, “Quantum state tomography with a single measurement setup,” Optica 4, 993–999 (2017).
[Crossref]

2016 (1)

G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, and C. Silberhorn, “Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics,” Phys. Rev. Lett. 116, 143601 (2016).
[Crossref]

2015 (6)

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
[Crossref]

P. A. Morris, R. S. Aspden, F. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
[Crossref]

D. J. Lum, S. H. Knarr, and J. C. Howell, “Fast Hadamard transforms for compressive sensing of joint systems: measurement of a 3.2 million-dimensional bi-photon probability distribution,” Opt. Express 23, 27636–27649 (2015).
[Crossref]

Z. Xie, T. Zhong, S. Shrestha, J. C. Bienfang, A. Restelli, F. N. C. Wong, and C. W. Wong, “Harnessing high dimensional hyper entanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
[Crossref]

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, 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]

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O. Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

2014 (2)

M. Mirhosseini, O. S. Magana-Loaiza, S. M. Hashemi Rafsanajani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
[Crossref]

J. Roslund, R. M. Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
[Crossref]

2013 (7)

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput. Optim. Appl. 56, 507–530 (2013).
[Crossref]

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

S. Etcheverry, G. Canas, E. S. Gomez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
[Crossref]

G. A. Howland and J. C. Howell, “Efficient high dimensional entanglement imaging with a compressive sensing double-pixel camera,” Phys. Rev. X 3, 011013 (2013).
[Crossref]

D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. P. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
[Crossref]

O. S. Magana-Loaiza, G. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
[Crossref]

N. Uribe-Patarroyo, A. Fraine, D. S. Simon, O. Minaeva, and A. V. Sergienko, “Object identification using correlated orbital angular momentum states,” Phys. Rev. Lett. 110, 043601 (2013).
[Crossref]

2012 (2)

W. T. Liu, T. Zhang, J. Y. Liu, P. X. Chen, and J. M. Yuan, “Experimental quantum state tomography via compressed sampling,” Phys. Rev. Lett. 108, 170403 (2012).
[Crossref]

P. B. Dixon, G. A. Howland, J. Schneeloch, and J. C. Howell, “Quantum mutual information capacity for high dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
[Crossref]

2011 (4)

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106, 100401 (2011).
[Crossref]

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84, 061804 (2011).
[Crossref]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Anderson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

T. Gerrits, M. J. Stevens, B. Baek, B. Calkins, A. Lita, S. Glancy, E. Knill, S. W. Nam, R. P. Mirin, R. H. Hadfield, R. S. Bennink, W. P. Grice, S. Dorenbos, T. Zijlstra, T. Klapwijk, and V. Zwiller, “Generation of degenerate, factorizable, pulsed squeezed light at telecom wavelengths,” Opt. Express 19, 24434–24447 (2011).
[Crossref]

2009 (2)

M. Avenhaus, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Fiber-assisted single-photon spectrograph,” Opt. Lett. 34, 2873–2875 (2009).
[Crossref]

A. Christ, K. Laiho, A. Eckstein, T. Lauckner, P. J. Mosley, and C. Silberhorn, “Spatial modes in waveguided parametric down-conversion,” Phys. Rev. A 80, 033829 (2009).
[Crossref]

2008 (1)

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101, 153602 (2008).
[Crossref]

2007 (3)

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. A 98, 060503 (2007).
[Crossref]

M. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[Crossref]

J. Mallon and P. F. Whelan, “Calibration and removal of lateral chromatic aberration in images,” Pattern Recogn. Lett. 28, 125–135 (2007).
[Crossref]

2005 (1)

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
[Crossref]

2004 (1)

J. C. Howell, R. S. Bennink, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum and position-entangled photons from spontaneous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref]

1997 (1)

1983 (1)

D. H. Auston, “Subpicosecond electro-optic shock waves,” Appl. Phys. Lett. 43, 713–715 (1983).
[Crossref]

Abouraddy, A. F.

L. Martin, D. Mardani, H. E. Kondakci, A. N. Vamivakas, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

Ali-Khan, I.

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. A 98, 060503 (2007).
[Crossref]

Almeida, M. P.

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106, 100401 (2011).
[Crossref]

Anderson, E.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Anderson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Araujo, R. M.

J. Roslund, R. M. Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
[Crossref]

Aspden, R. S.

P. A. Morris, R. S. Aspden, F. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
[Crossref]

Auston, D. H.

D. H. Auston, “Subpicosecond electro-optic shock waves,” Appl. Phys. Lett. 43, 713–715 (1983).
[Crossref]

Avenhaus, M.

Azana, J.

M. Kues, C. Reimer, P. Roztocki, L. Romero-Cortes, S. Sciara, B. Wetzel, L. Caspani, J. Azana, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Baek, B.

Bartley, T. J.

G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, and C. Silberhorn, “Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics,” Phys. Rev. Lett. 116, 143601 (2016).
[Crossref]

Bell, F. E. C.

P. A. Morris, R. S. Aspden, F. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
[Crossref]

Bennink, R. S.

Bienfang, J. C.

Z. Xie, T. Zhong, S. Shrestha, J. C. Bienfang, A. Restelli, F. N. C. Wong, and C. W. Wong, “Harnessing high dimensional hyper entanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
[Crossref]

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, 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]

Boyd, R. W.

Z. Yang, O. S. Magana-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. Hashemi Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light: Sci. Appl. 6, e17013 (2017).
[Crossref]

P. A. Morris, R. S. Aspden, F. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
[Crossref]

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O. Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

M. Mirhosseini, O. S. Magana-Loaiza, S. M. Hashemi Rafsanajani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
[Crossref]

O. S. Magana-Loaiza, G. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
[Crossref]

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84, 061804 (2011).
[Crossref]

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
[Crossref]

J. C. Howell, R. S. Bennink, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum and position-entangled photons from spontaneous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[Crossref]

Broadbent, C. J.

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. A 98, 060503 (2007).
[Crossref]

Broome, M. A.

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106, 100401 (2011).
[Crossref]

Buller, G. S.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Anderson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Calkins, B.

Canas, G.

S. Etcheverry, G. Canas, E. S. Gomez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
[Crossref]

Candes, M.

M. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[Crossref]

Caspani, L.

M. Kues, C. Reimer, P. Roztocki, L. Romero-Cortes, S. Sciara, B. Wetzel, L. Caspani, J. Azana, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Chan, K. W. C.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84, 061804 (2011).
[Crossref]

Chen, P. X.

W. T. Liu, T. Zhang, J. Y. Liu, P. X. Chen, and J. M. Yuan, “Experimental quantum state tomography via compressed sampling,” Phys. Rev. Lett. 108, 170403 (2012).
[Crossref]

Christ, A.

A. Christ, K. Laiho, A. Eckstein, T. Lauckner, P. J. Mosley, and C. Silberhorn, “Spatial modes in waveguided parametric down-conversion,” Phys. Rev. A 80, 033829 (2009).
[Crossref]

Dada, A. C.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Anderson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
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P. B. Dixon, G. A. Howland, J. Schneeloch, and J. C. Howell, “Quantum mutual information capacity for high dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
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Dudley, A.

D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. P. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
[Crossref]

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M. Avenhaus, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Fiber-assisted single-photon spectrograph,” Opt. Lett. 34, 2873–2875 (2009).
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A. Christ, K. Laiho, A. Eckstein, T. Lauckner, P. J. Mosley, and C. Silberhorn, “Spatial modes in waveguided parametric down-conversion,” Phys. Rev. A 80, 033829 (2009).
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J. Roslund, R. M. Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
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D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. P. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
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Z. Yang, O. S. Magana-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. Hashemi Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light: Sci. Appl. 6, e17013 (2017).
[Crossref]

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Z. Yang, O. S. Magana-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. Hashemi Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light: Sci. Appl. 6, e17013 (2017).
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M. Mirhosseini, O. S. Magana-Loaiza, M. N. O. Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
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G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, and C. Silberhorn, “Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics,” Phys. Rev. Lett. 116, 143601 (2016).
[Crossref]

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
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F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
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D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. P. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
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S. Etcheverry, G. Canas, E. S. Gomez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
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F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
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M. Mirhosseini, O. S. Magana-Loaiza, S. M. Hashemi Rafsanajani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
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Z. Yang, O. S. Magana-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. Hashemi Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light: Sci. Appl. 6, e17013 (2017).
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T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, 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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S. H. Knarr, D. J. Lum, J. Schneeloch, and J. C. Howell, “Compressive direct imaging of a billion-dimensional optical phase space,” Phys. Rev. A 98, 023854 (2018).
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D. J. Lum, S. H. Knarr, and J. C. Howell, “Fast Hadamard transforms for compressive sensing of joint systems: measurement of a 3.2 million-dimensional bi-photon probability distribution,” Opt. Express 23, 27636–27649 (2015).
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G. A. Howland and J. C. Howell, “Efficient high dimensional entanglement imaging with a compressive sensing double-pixel camera,” Phys. Rev. X 3, 011013 (2013).
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P. B. Dixon, G. A. Howland, J. Schneeloch, and J. C. Howell, “Quantum mutual information capacity for high dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
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J. Roslund, R. M. Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
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M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
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Knarr, S. H.

S. H. Knarr, D. J. Lum, J. Schneeloch, and J. C. Howell, “Compressive direct imaging of a billion-dimensional optical phase space,” Phys. Rev. A 98, 023854 (2018).
[Crossref]

D. J. Lum, S. H. Knarr, and J. C. Howell, “Fast Hadamard transforms for compressive sensing of joint systems: measurement of a 3.2 million-dimensional bi-photon probability distribution,” Opt. Express 23, 27636–27649 (2015).
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Kondakci, H. E.

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A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106, 100401 (2011).
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D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. P. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
[Crossref]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Anderson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
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T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, 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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C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput. Optim. Appl. 56, 507–530 (2013).
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S. Etcheverry, G. Canas, E. S. Gomez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
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Lita, A. E.

G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, and C. Silberhorn, “Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics,” Phys. Rev. Lett. 116, 143601 (2016).
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T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, 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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F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
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[Crossref]

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S. H. Knarr, D. J. Lum, J. Schneeloch, and J. C. Howell, “Compressive direct imaging of a billion-dimensional optical phase space,” Phys. Rev. A 98, 023854 (2018).
[Crossref]

D. J. Lum, S. H. Knarr, and J. C. Howell, “Fast Hadamard transforms for compressive sensing of joint systems: measurement of a 3.2 million-dimensional bi-photon probability distribution,” Opt. Express 23, 27636–27649 (2015).
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P. Mouroulis and J. Macdonald, Geometrical Optics Optical Design (Oxford University, 1997).

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Z. Yang, O. S. Magana-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. Hashemi Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light: Sci. Appl. 6, e17013 (2017).
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M. Mirhosseini, O. S. Magana-Loaiza, M. N. O. Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

M. Mirhosseini, O. S. Magana-Loaiza, S. M. Hashemi Rafsanajani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
[Crossref]

O. S. Magana-Loaiza, G. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
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M. Mirhosseini, O. S. Magana-Loaiza, M. N. O. Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
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O. S. Magana-Loaiza, G. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
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[Crossref]

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T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
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F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
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L. Martin, D. Mardani, H. E. Kondakci, A. N. Vamivakas, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
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Minaeva, O.

N. Uribe-Patarroyo, A. Fraine, D. S. Simon, O. Minaeva, and A. V. Sergienko, “Object identification using correlated orbital angular momentum states,” Phys. Rev. Lett. 110, 043601 (2013).
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Z. Yang, O. S. Magana-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. Hashemi Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light: Sci. Appl. 6, e17013 (2017).
[Crossref]

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O. Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
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M. Mirhosseini, O. S. Magana-Loaiza, S. M. Hashemi Rafsanajani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
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Mohseni, M.

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106, 100401 (2011).
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P. A. Morris, R. S. Aspden, F. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
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M. Avenhaus, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Fiber-assisted single-photon spectrograph,” Opt. Lett. 34, 2873–2875 (2009).
[Crossref]

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[Crossref]

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P. Mouroulis and J. Macdonald, Geometrical Optics Optical Design (Oxford University, 1997).

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G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, and C. Silberhorn, “Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics,” Phys. Rev. Lett. 116, 143601 (2016).
[Crossref]

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
[Crossref]

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
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S. Etcheverry, G. Canas, E. S. Gomez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
[Crossref]

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M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
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P. A. Morris, R. S. Aspden, F. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
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[Crossref]

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D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. P. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
[Crossref]

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A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106, 100401 (2011).
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Reimer, C.

M. Kues, C. Reimer, P. Roztocki, L. Romero-Cortes, S. Sciara, B. Wetzel, L. Caspani, J. Azana, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

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T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, 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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M. Mirhosseini, O. S. Magana-Loaiza, M. N. O. Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Romberg, J.

M. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[Crossref]

Romero, J.

D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. P. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
[Crossref]

Romero-Cortes, L.

M. Kues, C. Reimer, P. Roztocki, L. Romero-Cortes, S. Sciara, B. Wetzel, L. Caspani, J. Azana, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Roslund, J.

J. Roslund, R. M. Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
[Crossref]

Roztocki, P.

M. Kues, C. Reimer, P. Roztocki, L. Romero-Cortes, S. Sciara, B. Wetzel, L. Caspani, J. Azana, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Saavedra, C.

S. Etcheverry, G. Canas, E. S. Gomez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
[Crossref]

Schneeloch, J.

S. H. Knarr, D. J. Lum, J. Schneeloch, and J. C. Howell, “Compressive direct imaging of a billion-dimensional optical phase space,” Phys. Rev. A 98, 023854 (2018).
[Crossref]

P. B. Dixon, G. A. Howland, J. Schneeloch, and J. C. Howell, “Quantum mutual information capacity for high dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
[Crossref]

Sciara, S.

M. Kues, C. Reimer, P. Roztocki, L. Romero-Cortes, S. Sciara, B. Wetzel, L. Caspani, J. Azana, 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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Sergienko, A. V.

N. Uribe-Patarroyo, A. Fraine, D. S. Simon, O. Minaeva, and A. V. Sergienko, “Object identification using correlated orbital angular momentum states,” Phys. Rev. Lett. 110, 043601 (2013).
[Crossref]

Shabani, A.

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106, 100401 (2011).
[Crossref]

Shalm, L. K.

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
[Crossref]

Shaw, M.

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
[Crossref]

Shenoy, M. R.

Shrestha, S.

Z. Xie, T. Zhong, S. Shrestha, J. C. Bienfang, A. Restelli, F. N. C. Wong, and C. W. Wong, “Harnessing high dimensional hyper entanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
[Crossref]

Silberhorn, C.

G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, and C. Silberhorn, “Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics,” Phys. Rev. Lett. 116, 143601 (2016).
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A. Christ, K. Laiho, A. Eckstein, T. Lauckner, P. J. Mosley, and C. Silberhorn, “Spatial modes in waveguided parametric down-conversion,” Phys. Rev. A 80, 033829 (2009).
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N. Uribe-Patarroyo, A. Fraine, D. S. Simon, O. Minaeva, and A. V. Sergienko, “Object identification using correlated orbital angular momentum states,” Phys. Rev. Lett. 110, 043601 (2013).
[Crossref]

Stern, J. A.

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Stevens, M. J.

Sullivan, M. N. O.

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O. Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Thyagarajan, K.

Tovstonog, S.

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101, 153602 (2008).
[Crossref]

Treps, N.

J. Roslund, R. M. Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
[Crossref]

Uribe-Patarroyo, N.

N. Uribe-Patarroyo, A. Fraine, D. S. Simon, O. Minaeva, and A. V. Sergienko, “Object identification using correlated orbital angular momentum states,” Phys. Rev. Lett. 110, 043601 (2013).
[Crossref]

Vamivakas, A. N.

L. Martin, D. Mardani, H. E. Kondakci, A. N. Vamivakas, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

Vayshenker, I.

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Verma, V. B.

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, 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]

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
[Crossref]

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

Wetzel, B.

M. Kues, C. Reimer, P. Roztocki, L. Romero-Cortes, S. Sciara, B. Wetzel, L. Caspani, J. Azana, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Whelan, P. F.

J. Mallon and P. F. Whelan, “Calibration and removal of lateral chromatic aberration in images,” Pattern Recogn. Lett. 28, 125–135 (2007).
[Crossref]

White, A. G.

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106, 100401 (2011).
[Crossref]

Wong, C. W.

Z. Xie, T. Zhong, S. Shrestha, J. C. Bienfang, A. Restelli, F. N. C. Wong, and C. W. Wong, “Harnessing high dimensional hyper entanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
[Crossref]

Wong, F. N. C.

Z. Xie, T. Zhong, S. Shrestha, J. C. Bienfang, A. Restelli, F. N. C. Wong, and C. W. Wong, “Harnessing high dimensional hyper entanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
[Crossref]

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, 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]

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101, 153602 (2008).
[Crossref]

Xavier, G. B.

S. Etcheverry, G. Canas, E. S. Gomez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
[Crossref]

Xie, Z.

Z. Xie, T. Zhong, S. Shrestha, J. C. Bienfang, A. Restelli, F. N. C. Wong, and C. W. Wong, “Harnessing high dimensional hyper entanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
[Crossref]

Yang, Z.

Z. Yang, O. S. Magana-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. Hashemi Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light: Sci. Appl. 6, e17013 (2017).
[Crossref]

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C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput. Optim. Appl. 56, 507–530 (2013).
[Crossref]

Yuan, J. M.

W. T. Liu, T. Zhang, J. Y. Liu, P. X. Chen, and J. M. Yuan, “Experimental quantum state tomography via compressed sampling,” Phys. Rev. Lett. 108, 170403 (2012).
[Crossref]

Zerom, P.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84, 061804 (2011).
[Crossref]

Zhang, T.

W. T. Liu, T. Zhang, J. Y. Liu, P. X. Chen, and J. M. Yuan, “Experimental quantum state tomography via compressed sampling,” Phys. Rev. Lett. 108, 170403 (2012).
[Crossref]

Zhang, Y.

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput. Optim. Appl. 56, 507–530 (2013).
[Crossref]

Zhong, T.

Z. Xie, T. Zhong, S. Shrestha, J. C. Bienfang, A. Restelli, F. N. C. Wong, and C. W. Wong, “Harnessing high dimensional hyper entanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
[Crossref]

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, 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]

Zhou, H.

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, 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]

Zhou, Y.

Z. Yang, O. S. Magana-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. Hashemi Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light: Sci. Appl. 6, e17013 (2017).
[Crossref]

Zijlstra, T.

Zwiller, V.

Appl. Phys. Lett. (2)

O. S. Magana-Loaiza, G. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102, 231104 (2013).
[Crossref]

D. H. Auston, “Subpicosecond electro-optic shock waves,” Appl. Phys. Lett. 43, 713–715 (1983).
[Crossref]

Comput. Optim. Appl. (1)

C. Li, W. Yin, H. Jiang, and Y. Zhang, “An efficient augmented Lagrangian method with applications to total variation minimization,” Comput. Optim. Appl. 56, 507–530 (2013).
[Crossref]

Inverse Probl. (1)

M. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Probl. 23, 969–985 (2007).
[Crossref]

J. Opt. Soc. Am. B (1)

Light: Sci. Appl. (1)

Z. Yang, O. S. Magana-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. Hashemi Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light: Sci. Appl. 6, e17013 (2017).
[Crossref]

Nat. Commun. (1)

P. A. Morris, R. S. Aspden, F. E. C. Bell, R. W. Boyd, and M. J. Padgett, “Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
[Crossref]

Nat. Photonics (3)

F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, and S. W. Nam, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214 (2013).
[Crossref]

J. Roslund, R. M. Araujo, S. Jiang, C. Fabre, and N. Treps, “Wavelength-multiplexed quantum networks with ultrafast frequency combs,” Nat. Photonics 8, 109–112 (2014).
[Crossref]

Z. Xie, T. Zhong, S. Shrestha, J. C. Bienfang, A. Restelli, F. N. C. Wong, and C. W. Wong, “Harnessing high dimensional hyper entanglement through a biphoton frequency comb,” Nat. Photonics 9, 536–542 (2015).
[Crossref]

Nat. Phys. (1)

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Anderson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Nature (1)

M. Kues, C. Reimer, P. Roztocki, L. Romero-Cortes, S. Sciara, B. Wetzel, L. Caspani, J. Azana, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

New J. Phys. (2)

T. Zhong, H. Zhou, R. D. Horansky, C. Lee, V. B. Verma, A. E. Lita, A. Restelli, J. C. Bienfang, 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]

M. Mirhosseini, O. S. Magana-Loaiza, M. N. O. Sullivan, B. Rodenburg, M. Malik, M. P. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Optica (1)

Pattern Recogn. Lett. (1)

J. Mallon and P. F. Whelan, “Calibration and removal of lateral chromatic aberration in images,” Pattern Recogn. Lett. 28, 125–135 (2007).
[Crossref]

Phys. Rev. A (5)

A. Christ, K. Laiho, A. Eckstein, T. Lauckner, P. J. Mosley, and C. Silberhorn, “Spatial modes in waveguided parametric down-conversion,” Phys. Rev. A 80, 033829 (2009).
[Crossref]

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
[Crossref]

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84, 061804 (2011).
[Crossref]

I. Ali-Khan, C. J. Broadbent, and J. C. Howell, “Large alphabet quantum key distribution using energy-time entangled bipartite states,” Phys. Rev. A 98, 060503 (2007).
[Crossref]

S. H. Knarr, D. J. Lum, J. Schneeloch, and J. C. Howell, “Compressive direct imaging of a billion-dimensional optical phase space,” Phys. Rev. A 98, 023854 (2018).
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Phys. Rev. Lett. (10)

M. N. O’Sullivan-Hale, I. A. Khan, R. W. Boyd, and J. C. Howell, “Pixel entanglement: experimental realization of optically entangled d = 3 and d = 6 qudits,” Phys. Rev. Lett. 94, 220501 (2005).
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M. Mirhosseini, O. S. Magana-Loaiza, S. M. Hashemi Rafsanajani, and R. W. Boyd, “Compressive direct measurement of the quantum wave function,” Phys. Rev. Lett. 113, 090402 (2014).
[Crossref]

P. B. Dixon, G. A. Howland, J. Schneeloch, and J. C. Howell, “Quantum mutual information capacity for high dimensional entangled states,” Phys. Rev. Lett. 108, 143603 (2012).
[Crossref]

W. T. Liu, T. Zhang, J. Y. Liu, P. X. Chen, and J. M. Yuan, “Experimental quantum state tomography via compressed sampling,” Phys. Rev. Lett. 108, 170403 (2012).
[Crossref]

A. Shabani, R. L. Kosut, M. Mohseni, H. Rabitz, M. A. Broome, M. P. Almeida, A. Fedrizzi, and A. G. White, “Efficient measurement of quantum dynamics via compressive sensing,” Phys. Rev. Lett. 106, 100401 (2011).
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J. C. Howell, R. S. Bennink, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum and position-entangled photons from spontaneous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
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D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. P. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
[Crossref]

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. 101, 153602 (2008).
[Crossref]

N. Uribe-Patarroyo, A. Fraine, D. S. Simon, O. Minaeva, and A. V. Sergienko, “Object identification using correlated orbital angular momentum states,” Phys. Rev. Lett. 110, 043601 (2013).
[Crossref]

G. Harder, T. J. Bartley, A. E. Lita, S. W. Nam, T. Gerrits, and C. Silberhorn, “Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics,” Phys. Rev. Lett. 116, 143601 (2016).
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Phys. Rev. X (1)

G. A. Howland and J. C. Howell, “Efficient high dimensional entanglement imaging with a compressive sensing double-pixel camera,” Phys. Rev. X 3, 011013 (2013).
[Crossref]

Sci. Rep. (2)

L. Martin, D. Mardani, H. E. Kondakci, A. N. Vamivakas, and A. F. Abouraddy, “Basis-neutral Hilbert-space analyzers,” Sci. Rep. 7, 44995 (2017).
[Crossref]

S. Etcheverry, G. Canas, E. S. Gomez, W. A. T. Nogueira, C. Saavedra, G. B. Xavier, and G. Lima, “Quantum key distribution session with 16-dimensional photonic states,” Sci. Rep. 3, 2316 (2013).
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P. Mouroulis and J. Macdonald, Geometrical Optics Optical Design (Oxford University, 1997).

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Figures (5)

Fig. 1.
Fig. 1. Experimental setup. Photon pairs at telecom wavelength (λSPDC=1570  nm) are generated in a Rb:PPKTP waveguide through a type II SPDC process. The spatial reconstruction is performed by probing the signal and idler photons using a DMD displaying a series of random patterns. Reflected photons are then imaged with a telescope and spatially separated by a PBS. We simultaneously obtain spatial and spectral information by using 10 km of fiber that allows us to map frequency to time. Finally, we utilize SNSPDs and a fast TTM to detect photons and record times of arrival. A small portion of the pump is separated by a beam splitter and detected by a fast photodiode. We use the signal from the photodiode to trigger our TTM, which is used to count downconverted photons.
Fig. 2.
Fig. 2. Spatial profile of (a) signal and (b) idler reconstructed using a sampling ratio of 20%. The sensing matrix contains N=64×64=4096 elements. (c) shows the reconstructed joint spatial distribution obtained through coincidences between signal and idler photons.
Fig. 3.
Fig. 3. (a) Joint photon arrival time. (b) Full marginal spectra of signal and idler photons with phase matching peak at 1570 nm (inset). (c) and (d) Reconstructed spatial profiles for signal and idler photons for shorter wavelengths generated due to a slightly multimode pump spectrum.
Fig. 4.
Fig. 4. (a) Spatiospectral reconstructions of signal and idler photons. These marginal distributions are obtained within the main phase-matched peak using a sampling ratio of 20% and sensing matrices with 64×64 pixels. (b) The joint spectral intensity distributions are plotted by spectrally resolving the coincidences between the signal and idler photons into 15 bins, each within its respective bandwidths of the main phase-matched peak. Each frame on the plot corresponds to a spatial reconstruction on a 64×64 sensing array. This is obtained by integrating over the coincidences measured within individual spectral bins. The integration time required per pattern of the CS measurement was set to 4 s.
Fig. 5.
Fig. 5. Fidelity of the reconstructed high-dimensional state as a function of number of measurements.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

|Ψ=ω=1Dωfω|ωs|ωij=1Djsj|xjs|xji,
|ϕ=A^|Ψ=ω=1DωT^fω|ωs|ωij=1DjO^sj|xjs|xji.
|ϕ=t=1Dtf^t|ts|tij=1DjlO^m,lsj|xls|xli.
(ϕ1ϕ2ϕM)=(A1,1A1,2A1,NA2,1A2,2A2,NAM,1AM,2AM,N)(ψ1ψ2ψN).
minΨlΨl1+μ2A^Ψ^ϕ^|22.