Abstract

We demonstrate a tried-and-true binary strategy for angular displacement estimation, of which the measuring system is a modified Mach-Zehnder interferometer fed by a coherent state carrying orbital angular momentum, and two Dove prisms are embedded in two arms. Unlike previous protocols, in this paper, we use fidelity instead of standard deviation to evaluate the detection strategies. Two binary strategy candidates, parity detection and Z detection, are considered and compared. In addition, we study the effects of several realistic scenarios on the estimation protocol, including transmission loss, detection efficiency, dark counts, and those which are a combination thereof. Finally, we exhibit a proof-of-principle experiment, the results suggest a resolution enhancement effect with a factor of 3.72.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2017 (5)

Z. Zhang, T. Qiao, L. Cen, J. Zhang, F. Wang, and Y. Zhao, “Optimal quantum detection strategy for super-resolving angular-rotation measurement,” Appl. Phys. B 123, 148 (2017).
[Crossref]

P. Liu, P. Wang, W. Yang, G. Jin, and C. Sun, “Fisher information of a squeezed-state interferometer with a finite photon-number resolution,” Phys. Rev. A 95, 023824 (2017).
[Crossref]

J. Zhang, Z. Zhang, L. Cen, M. Yu, S. Li, F. Wang, and Y. Zhao, “Effects of imperfect elements on resolution and sensitivity of quantum metrology using two-mode squeezed vacuum state,” Opt. Express 25, 24907–24916 (2017).
[Crossref] [PubMed]

B. T. Gard, C. You, D. K. Mishra, R. Singh, H. Lee, T. R. Corbitt, and J. P. Dowling, “Nearly optimal measurement schemes in a noisy Mach-Zehnder interferometer with coherent and squeezed vacuum,” EPJ Quantum Technol. 4, 4 (2017).
[Crossref]

Z. Huang, K. R. Motes, P. M. Anisimov, J. P. Dowling, and D. W. Berry, “Adaptive phase estimation with two-mode squeezed vacuum and parity measurement,” Phys. Rev. A 95, 053837 (2017).
[Crossref]

2016 (1)

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2e1501165 (2016).
[Crossref]

2015 (1)

2014 (5)

2013 (6)

M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry using a laser power source,” Phys. Rev. Lett. 111, 173601 (2013).
[Crossref] [PubMed]

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref] [PubMed]

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] [PubMed]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
[Crossref] [PubMed]

2011 (3)

B. Escher, R. de Matos Filho, and L. Davidovich, “Quantum metrology for noisy systems,” Braz. J. Phys. 41, 229–247 (2011).
[Crossref]

T. B. Bahder, “Phase estimation with nonunitary interferometers: Information as a metric,” Phys. Rev. A 83, 053601 (2011).
[Crossref]

A. Datta, L. Zhang, N. Thomas-Peter, U. Dorner, B. J. Smith, and I. A. Walmsley, “Quantum metrology with imperfect states and detectors,” Phys. Rev. A 83, 063836 (2011).
[Crossref]

2010 (3)

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photon. 4, 357–360 (2010).
[Crossref]

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010).
[Crossref]

P. Zhang, B.-H. Liu, R.-F. Liu, H.-R. Li, F.-L. Li, and G.-C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A 81, 052322 (2010).
[Crossref]

2008 (2)

D. Simon, A. Sergienko, and T. Bahder, “Dispersion and fidelity in quantum interferometry,” Phys. Rev. A 78, 053829 (2008).
[Crossref]

J. P. Dowling, “Quantum optical metrology–the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).
[Crossref]

2007 (1)

P. Zhang, X.-F. Ren, X.-B. Zou, B.-H. Liu, Y.-F. Huang, and G.-C. Guo, “Demonstration of one-dimensional quantum random walks using orbital angular momentum of photons,” Phys. Rev. A 75, 052310 (2007).
[Crossref]

2006 (3)

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[Crossref] [PubMed]

T. B. Bahder and P. A. Lopata, “Fidelity of quantum interferometers,” Phys. Rev. A 74, 051801 (2006).
[Crossref]

L. Pezzé and A. Smerzi, “Phase sensitivity of a Mach-Zehnder interferometer,” Phys. Rev. A 73, 011801 (2006).
[Crossref]

2004 (1)

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004).
[Crossref]

2002 (1)

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

1998 (1)

T. Kim, O. Pfister, M. J. Holland, J. Noh, and J. L. Hall, “Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons,” Phys. Rev. A 57, 4004 (1998).
[Crossref]

1996 (1)

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649 (1996).
[Crossref] [PubMed]

1994 (1)

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

1986 (1)

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1, 1) interferometers,” Phys. Rev. A 33, 4033 (1986).
[Crossref]

Achilles, D.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004).
[Crossref]

Agnew, M.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2e1501165 (2016).
[Crossref]

Ahmed, N.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[Crossref] [PubMed]

Anisimov, P. M.

Z. Huang, K. R. Motes, P. M. Anisimov, J. P. Dowling, and D. W. Berry, “Adaptive phase estimation with two-mode squeezed vacuum and parity measurement,” Phys. Rev. A 95, 053837 (2017).
[Crossref]

Aolita, L.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

Ashrafi, N.

Ashrafi, S.

Bahder, T.

D. Simon, A. Sergienko, and T. Bahder, “Dispersion and fidelity in quantum interferometry,” Phys. Rev. A 78, 053829 (2008).
[Crossref]

Bahder, T. B.

T. B. Bahder, “Phase estimation with nonunitary interferometers: Information as a metric,” Phys. Rev. A 83, 053601 (2011).
[Crossref]

T. B. Bahder and P. A. Lopata, “Fidelity of quantum interferometers,” Phys. Rev. A 74, 051801 (2006).
[Crossref]

Banaszek, K.

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photon. 4, 357–360 (2010).
[Crossref]

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004).
[Crossref]

Bao, C.

Barnett, S. M.

M. P. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1, 1–4 (2014).
[Crossref]

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Berry, D. W.

Z. Huang, K. R. Motes, P. M. Anisimov, J. P. Dowling, and D. W. Berry, “Adaptive phase estimation with two-mode squeezed vacuum and parity measurement,” Phys. Rev. A 95, 053837 (2017).
[Crossref]

Bollinger, J. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649 (1996).
[Crossref] [PubMed]

Boyd, R. W.

O. S. Magaña Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112, 200401 (2014).
[Crossref]

Cao, Y.

Caves, C. M.

M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry using a laser power source,” Phys. Rev. Lett. 111, 173601 (2013).
[Crossref] [PubMed]

Cen, L.

Z. Zhang, T. Qiao, L. Cen, J. Zhang, F. Wang, and Y. Zhao, “Optimal quantum detection strategy for super-resolving angular-rotation measurement,” Appl. Phys. B 123, 148 (2017).
[Crossref]

J. Zhang, Z. Zhang, L. Cen, M. Yu, S. Li, F. Wang, and Y. Zhao, “Effects of imperfect elements on resolution and sensitivity of quantum metrology using two-mode squeezed vacuum state,” Opt. Express 25, 24907–24916 (2017).
[Crossref] [PubMed]

Cladé, P.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[Crossref] [PubMed]

Cohen, L.

Corbitt, T. R.

B. T. Gard, C. You, D. K. Mishra, R. Singh, H. Lee, T. R. Corbitt, and J. P. Dowling, “Nearly optimal measurement schemes in a noisy Mach-Zehnder interferometer with coherent and squeezed vacuum,” EPJ Quantum Technol. 4, 4 (2017).
[Crossref]

D’ambrosio, V.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

Datta, A.

A. Datta, L. Zhang, N. Thomas-Peter, U. Dorner, B. J. Smith, and I. A. Walmsley, “Quantum metrology with imperfect states and detectors,” Phys. Rev. A 83, 063836 (2011).
[Crossref]

Davidovich, L.

B. Escher, R. de Matos Filho, and L. Davidovich, “Quantum metrology for noisy systems,” Braz. J. Phys. 41, 229–247 (2011).
[Crossref]

de Matos Filho, R.

B. Escher, R. de Matos Filho, and L. Davidovich, “Quantum metrology for noisy systems,” Braz. J. Phys. 41, 229–247 (2011).
[Crossref]

Del Re, L.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

Demkowicz-Dobrzanski, R.

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photon. 4, 357–360 (2010).
[Crossref]

Dorner, U.

A. Datta, L. Zhang, N. Thomas-Peter, U. Dorner, B. J. Smith, and I. A. Walmsley, “Quantum metrology with imperfect states and detectors,” Phys. Rev. A 83, 063836 (2011).
[Crossref]

Dovrat, L.

Dowling, J. P.

Z. Huang, K. R. Motes, P. M. Anisimov, J. P. Dowling, and D. W. Berry, “Adaptive phase estimation with two-mode squeezed vacuum and parity measurement,” Phys. Rev. A 95, 053837 (2017).
[Crossref]

B. T. Gard, C. You, D. K. Mishra, R. Singh, H. Lee, T. R. Corbitt, and J. P. Dowling, “Nearly optimal measurement schemes in a noisy Mach-Zehnder interferometer with coherent and squeezed vacuum,” EPJ Quantum Technol. 4, 4 (2017).
[Crossref]

J. P. Dowling, “Quantum optical metrology–the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).
[Crossref]

Dudley, A.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Eisenberg, H.

Eisenberg, H. S.

Escher, B.

B. Escher, R. de Matos Filho, and L. Davidovich, “Quantum metrology for noisy systems,” Braz. J. Phys. 41, 229–247 (2011).
[Crossref]

Feng, X.

X. Feng, G. Jin, and W. Yang, “Quantum interferometry with binary-outcome measurements in the presence of phase diffusion,” Phys. Rev. A 90, 013807 (2014).
[Crossref]

Fitch, M. J.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004).
[Crossref]

Forbes, A.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2e1501165 (2016).
[Crossref]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
[Crossref] [PubMed]

Fraine, A.

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] [PubMed]

Franson, J. D.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004).
[Crossref]

Gard, B. T.

B. T. Gard, C. You, D. K. Mishra, R. Singh, H. Lee, T. R. Corbitt, and J. P. Dowling, “Nearly optimal measurement schemes in a noisy Mach-Zehnder interferometer with coherent and squeezed vacuum,” EPJ Quantum Technol. 4, 4 (2017).
[Crossref]

Gerry, C. C.

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010).
[Crossref]

Giovannini, D.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Goyal, S.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Goyal, S. K.

S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
[Crossref] [PubMed]

Guo, G.-C.

P. Zhang, B.-H. Liu, R.-F. Liu, H.-R. Li, F.-L. Li, and G.-C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A 81, 052322 (2010).
[Crossref]

P. Zhang, X.-F. Ren, X.-B. Zou, B.-H. Liu, Y.-F. Huang, and G.-C. Guo, “Demonstration of one-dimensional quantum random walks using orbital angular momentum of photons,” Phys. Rev. A 75, 052310 (2007).
[Crossref]

Hall, J. L.

T. Kim, O. Pfister, M. J. Holland, J. Noh, and J. L. Hall, “Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons,” Phys. Rev. A 57, 4004 (1998).
[Crossref]

Heinzen, D.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649 (1996).
[Crossref] [PubMed]

Hell, S. W.

Helmerson, K.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[Crossref] [PubMed]

Holland, M. J.

T. Kim, O. Pfister, M. J. Holland, J. Noh, and J. L. Hall, “Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons,” Phys. Rev. A 57, 4004 (1998).
[Crossref]

Huang, H.

Huang, Y.-F.

P. Zhang, X.-F. Ren, X.-B. Zou, B.-H. Liu, Y.-F. Huang, and G.-C. Guo, “Demonstration of one-dimensional quantum random walks using orbital angular momentum of photons,” Phys. Rev. A 75, 052310 (2007).
[Crossref]

Huang, Z.

Z. Huang, K. R. Motes, P. M. Anisimov, J. P. Dowling, and D. W. Berry, “Adaptive phase estimation with two-mode squeezed vacuum and parity measurement,” Phys. Rev. A 95, 053837 (2017).
[Crossref]

Istrati, D.

Itano, W. M.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649 (1996).
[Crossref] [PubMed]

Jacobs, B. C.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004).
[Crossref]

Jin, G.

P. Liu, P. Wang, W. Yang, G. Jin, and C. Sun, “Fisher information of a squeezed-state interferometer with a finite photon-number resolution,” Phys. Rev. A 95, 023824 (2017).
[Crossref]

X. Feng, G. Jin, and W. Yang, “Quantum interferometry with binary-outcome measurements in the presence of phase diffusion,” Phys. Rev. A 90, 013807 (2014).
[Crossref]

Kacprowicz, M.

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photon. 4, 357–360 (2010).
[Crossref]

Kim, T.

T. Kim, O. Pfister, M. J. Holland, J. Noh, and J. L. Hall, “Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons,” Phys. Rev. A 57, 4004 (1998).
[Crossref]

Klauder, J. R.

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1, 1) interferometers,” Phys. Rev. A 33, 4033 (1986).
[Crossref]

Konrad, T.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2e1501165 (2016).
[Crossref]

S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
[Crossref] [PubMed]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Kwek, L. C.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

Lang, M. D.

M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry using a laser power source,” Phys. Rev. Lett. 111, 173601 (2013).
[Crossref] [PubMed]

Lavery, M. P.

M. P. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1, 1–4 (2014).
[Crossref]

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref] [PubMed]

Lavery, M. P. J.

Leach, J.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2e1501165 (2016).
[Crossref]

Lee, H.

B. T. Gard, C. You, D. K. Mishra, R. Singh, H. Lee, T. R. Corbitt, and J. P. Dowling, “Nearly optimal measurement schemes in a noisy Mach-Zehnder interferometer with coherent and squeezed vacuum,” EPJ Quantum Technol. 4, 4 (2017).
[Crossref]

Li, F.-L.

P. Zhang, B.-H. Liu, R.-F. Liu, H.-R. Li, F.-L. Li, and G.-C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A 81, 052322 (2010).
[Crossref]

Li, H.-R.

P. Zhang, B.-H. Liu, R.-F. Liu, H.-R. Li, F.-L. Li, and G.-C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A 81, 052322 (2010).
[Crossref]

Li, L.

Li, S.

Li, Y.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

Liu, B.-H.

P. Zhang, B.-H. Liu, R.-F. Liu, H.-R. Li, F.-L. Li, and G.-C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A 81, 052322 (2010).
[Crossref]

P. Zhang, X.-F. Ren, X.-B. Zou, B.-H. Liu, Y.-F. Huang, and G.-C. Guo, “Demonstration of one-dimensional quantum random walks using orbital angular momentum of photons,” Phys. Rev. A 75, 052310 (2007).
[Crossref]

Liu, P.

P. Liu, P. Wang, W. Yang, G. Jin, and C. Sun, “Fisher information of a squeezed-state interferometer with a finite photon-number resolution,” Phys. Rev. A 95, 023824 (2017).
[Crossref]

Liu, R.-F.

P. Zhang, B.-H. Liu, R.-F. Liu, H.-R. Li, F.-L. Li, and G.-C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A 81, 052322 (2010).
[Crossref]

Lopata, P. A.

T. B. Bahder and P. A. Lopata, “Fidelity of quantum interferometers,” Phys. Rev. A 74, 051801 (2006).
[Crossref]

Lütkenhaus, N.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Mafu, M.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Magaña Loaiza, O. S.

O. S. Magaña Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112, 200401 (2014).
[Crossref]

Marrucci, L.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

McCall, S. L.

B. Yurke, S. L. McCall, and J. R. Klauder, “SU(2) and SU(1, 1) interferometers,” Phys. Rev. A 33, 4033 (1986).
[Crossref]

McLaren, M.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Mimih, J.

C. C. Gerry and J. Mimih, “The parity operator in quantum optical metrology,” Contemp. Phys. 51, 497–511 (2010).
[Crossref]

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).
[Crossref] [PubMed]

Mirhosseini, M.

O. S. Magaña Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112, 200401 (2014).
[Crossref]

Mishra, D. K.

B. T. Gard, C. You, D. K. Mishra, R. Singh, H. Lee, T. R. Corbitt, and J. P. Dowling, “Nearly optimal measurement schemes in a noisy Mach-Zehnder interferometer with coherent and squeezed vacuum,” EPJ Quantum Technol. 4, 4 (2017).
[Crossref]

Molisch, A. F.

Motes, K. R.

Z. Huang, K. R. Motes, P. M. Anisimov, J. P. Dowling, and D. W. Berry, “Adaptive phase estimation with two-mode squeezed vacuum and parity measurement,” Phys. Rev. A 95, 053837 (2017).
[Crossref]

Natarajan, V.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[Crossref] [PubMed]

Noh, J.

T. Kim, O. Pfister, M. J. Holland, J. Noh, and J. L. Hall, “Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons,” Phys. Rev. A 57, 4004 (1998).
[Crossref]

Padgett, M. J.

M. P. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1, 1–4 (2014).
[Crossref]

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref] [PubMed]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Petruccione, F.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Pezze, L.

L. Pezze and A. Smerzi, “Mach Zehnder interferometry with NOON quantum states,” arXiv preprint quant-ph/0508158 (2005).

Pezzé, L.

L. Pezzé and A. Smerzi, “Phase sensitivity of a Mach-Zehnder interferometer,” Phys. Rev. A 73, 011801 (2006).
[Crossref]

Pfister, O.

T. Kim, O. Pfister, M. J. Holland, J. Noh, and J. L. Hall, “Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons,” Phys. Rev. A 57, 4004 (1998).
[Crossref]

Phillips, W. D.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[Crossref] [PubMed]

Pittman, T. B.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004).
[Crossref]

Qiao, T.

Z. Zhang, T. Qiao, L. Cen, J. Zhang, F. Wang, and Y. Zhao, “Optimal quantum detection strategy for super-resolving angular-rotation measurement,” Appl. Phys. B 123, 148 (2017).
[Crossref]

Ramachandran, S.

Ren, X.-F.

P. Zhang, X.-F. Ren, X.-B. Zou, B.-H. Liu, Y.-F. Huang, and G.-C. Guo, “Demonstration of one-dimensional quantum random walks using orbital angular momentum of photons,” Phys. Rev. A 75, 052310 (2007).
[Crossref]

Ren, Y.

Rodenburg, B.

O. S. Magaña Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112, 200401 (2014).
[Crossref]

Roux, F. S.

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2e1501165 (2016).
[Crossref]

S. K. Goyal, F. S. Roux, A. Forbes, and T. Konrad, “Implementing quantum walks using orbital angular momentum of classical light,” Phys. Rev. Lett. 110, 263602 (2013).
[Crossref] [PubMed]

Ryu, C.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[Crossref] [PubMed]

Sciarrino, F.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

Sergienko, A.

D. Simon, A. Sergienko, and T. Bahder, “Dispersion and fidelity in quantum interferometry,” Phys. Rev. A 78, 053829 (2008).
[Crossref]

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] [PubMed]

Silberhorn, C.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004).
[Crossref]

Simon, D.

D. Simon, A. Sergienko, and T. Bahder, “Dispersion and fidelity in quantum interferometry,” Phys. Rev. A 78, 053829 (2008).
[Crossref]

Simon, D. S.

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] [PubMed]

Singh, R.

B. T. Gard, C. You, D. K. Mishra, R. Singh, H. Lee, T. R. Corbitt, and J. P. Dowling, “Nearly optimal measurement schemes in a noisy Mach-Zehnder interferometer with coherent and squeezed vacuum,” EPJ Quantum Technol. 4, 4 (2017).
[Crossref]

Sliwa, C.

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004).
[Crossref]

Slussarenko, S.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

Smerzi, A.

L. Pezzé and A. Smerzi, “Phase sensitivity of a Mach-Zehnder interferometer,” Phys. Rev. A 73, 011801 (2006).
[Crossref]

L. Pezze and A. Smerzi, “Mach Zehnder interferometry with NOON quantum states,” arXiv preprint quant-ph/0508158 (2005).

Smith, B. J.

A. Datta, L. Zhang, N. Thomas-Peter, U. Dorner, B. J. Smith, and I. A. Walmsley, “Quantum metrology with imperfect states and detectors,” Phys. Rev. A 83, 063836 (2011).
[Crossref]

Spagnolo, N.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

Speirits, F. C.

M. P. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1, 1–4 (2014).
[Crossref]

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref] [PubMed]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Sun, C.

P. Liu, P. Wang, W. Yang, G. Jin, and C. Sun, “Fisher information of a squeezed-state interferometer with a finite photon-number resolution,” Phys. Rev. A 95, 023824 (2017).
[Crossref]

Thomas-Peter, N.

A. Datta, L. Zhang, N. Thomas-Peter, U. Dorner, B. J. Smith, and I. A. Walmsley, “Quantum metrology with imperfect states and detectors,” Phys. Rev. A 83, 063836 (2011).
[Crossref]

Tur, M.

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] [PubMed]

Vaziri, A.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[Crossref] [PubMed]

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
[Crossref] [PubMed]

Walborn, S. P.

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

Walmsley, I.

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photon. 4, 357–360 (2010).
[Crossref]

Walmsley, I. A.

A. Datta, L. Zhang, N. Thomas-Peter, U. Dorner, B. J. Smith, and I. A. Walmsley, “Quantum metrology with imperfect states and detectors,” Phys. Rev. A 83, 063836 (2011).
[Crossref]

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004).
[Crossref]

Wang, F.

Z. Zhang, T. Qiao, L. Cen, J. Zhang, F. Wang, and Y. Zhao, “Optimal quantum detection strategy for super-resolving angular-rotation measurement,” Appl. Phys. B 123, 148 (2017).
[Crossref]

J. Zhang, Z. Zhang, L. Cen, M. Yu, S. Li, F. Wang, and Y. Zhao, “Effects of imperfect elements on resolution and sensitivity of quantum metrology using two-mode squeezed vacuum state,” Opt. Express 25, 24907–24916 (2017).
[Crossref] [PubMed]

Wang, J.

Wang, P.

P. Liu, P. Wang, W. Yang, G. Jin, and C. Sun, “Fisher information of a squeezed-state interferometer with a finite photon-number resolution,” Phys. Rev. A 95, 023824 (2017).
[Crossref]

Wasilewski, W.

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photon. 4, 357–360 (2010).
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X. Feng, G. Jin, and W. Yang, “Quantum interferometry with binary-outcome measurements in the presence of phase diffusion,” Phys. Rev. A 90, 013807 (2014).
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B. T. Gard, C. You, D. K. Mishra, R. Singh, H. Lee, T. R. Corbitt, and J. P. Dowling, “Nearly optimal measurement schemes in a noisy Mach-Zehnder interferometer with coherent and squeezed vacuum,” EPJ Quantum Technol. 4, 4 (2017).
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Adv. Opt. Photon. (1)

Appl. Phys. B (1)

Z. Zhang, T. Qiao, L. Cen, J. Zhang, F. Wang, and Y. Zhao, “Optimal quantum detection strategy for super-resolving angular-rotation measurement,” Appl. Phys. B 123, 148 (2017).
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Braz. J. Phys. (1)

B. Escher, R. de Matos Filho, and L. Davidovich, “Quantum metrology for noisy systems,” Braz. J. Phys. 41, 229–247 (2011).
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Contemp. Phys. (2)

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J. P. Dowling, “Quantum optical metrology–the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).
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EPJ Quantum Technol. (1)

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J. Mod. Opt. (1)

D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, I. A. Walmsley, M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number-resolving detection using time-multiplexing,” J. Mod. Opt. 51, 1499–1515 (2004).
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Nat. Commun. (1)

V. D’ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 42432 (2013).

Nat. Photon. (1)

M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift,” Nat. Photon. 4, 357–360 (2010).
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Opt. Express (3)

Opt. Lett. (1)

Optica (1)

Phys. Rev. A (15)

P. Zhang, B.-H. Liu, R.-F. Liu, H.-R. Li, F.-L. Li, and G.-C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A 81, 052322 (2010).
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M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
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P. Zhang, X.-F. Ren, X.-B. Zou, B.-H. Liu, Y.-F. Huang, and G.-C. Guo, “Demonstration of one-dimensional quantum random walks using orbital angular momentum of photons,” Phys. Rev. A 75, 052310 (2007).
[Crossref]

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P. Liu, P. Wang, W. Yang, G. Jin, and C. Sun, “Fisher information of a squeezed-state interferometer with a finite photon-number resolution,” Phys. Rev. A 95, 023824 (2017).
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X. Feng, G. Jin, and W. Yang, “Quantum interferometry with binary-outcome measurements in the presence of phase diffusion,” Phys. Rev. A 90, 013807 (2014).
[Crossref]

Phys. Rev. Lett. (6)

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett. 89, 240401 (2002).
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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).
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Sci. Adv. (1)

Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2e1501165 (2016).
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Science (1)

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
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Figures (8)

Fig. 1
Fig. 1 Schematic of an angular displacement estimation protocol. The inset is intensity distribution of modulated OAM beam obtained by a CCD camera. The optical elements are abbreviated as: L, laser; SMF, single-mode fiber; P, polarizer; FC, fiber coupler; SPP, spiral phase plate; HWP, half wave plate; PBS, polarizing beam splitter; DP, Dove prism; RM, reflection mirror; D, detector.
Fig. 2
Fig. 2 Conditional probability density p(θ|m) against angular displacement θ in the case of N = 1, = 3, and p(θ) = 1/2π. PD, parity detection; ZD, Z detection.
Fig. 3
Fig. 3 The fidelity H against the mean photon number N, where N ranges from 1 to 20, is an arbitrary integer, and p(θ) = 1/2π.
Fig. 4
Fig. 4 The fidelity H against transmission losses of the two paths, LA and LB, where both LA and LB range from 0 to 1 and N = 3. The color bar represents the corresponding values of the fidelity.
Fig. 5
Fig. 5 The fidelity H against detection efficiency η, where η ranges from 5% to 100% and N = 3.
Fig. 6
Fig. 6 The fidelity H against the mean photon number N and the rate of dark counts r, the range of r is between 10−8 and 10−2, N ranges from 1 to 10.
Fig. 7
Fig. 7 Probability of zero count (normalized measuring counts) against angular displacement. The solid red dots are experimental measuring data, while the solid blue line is a fit to the data. For each error bar, its mean value is calculated from the trials of M = 40000, its standard deviation is calculated by dividing these trials into 20 sets (M = 2000 in each set).
Fig. 8
Fig. 8 The posteriori distribution p(θ|θ*) against angular displacement θ, where actual value θ* sits at 0.0698. The numbers of trials for blue dashed line, red dash-dotted line, and green dotted line are 200, 500, and 100; the corresponding numbers of zero count are 167, 419, and 841, respectively.

Equations (19)

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| ψ = | i α cos ( θ ) A | i α sin ( θ ) B .
| ψ = e N 2 x , y = 0 [ i α cos ( θ ) ] x [ i α sin ( θ ) ] y x ! y ! | x A | y B ,
p ( zero | θ ) = exp [ N sin 2 ( θ ) ] ,
p ( nonzero | θ ) = 1 exp [ N sin 2 ( θ ) ] .
p ( even | θ ) = 1 2 { 1 + exp [ 2 N sin 2 ( θ ) ] } ,
p ( odd | θ ) = 1 2 { 1 exp [ 2 N sin 2 ( θ ) ] } .
p ( θ | m ) = p ( m | θ ) p ( θ ) π π d θ p ( m | θ ) p ( θ ) ,
H = m π π d θ p ( m | θ ) p ( θ ) log 2 [ p ( m | θ ) π π d θ p ( m | θ ) p ( θ ) ] .
| ψ B = | i α ( T A e i θ T B e i θ ) / 2 .
p 1 ( zero | θ ) = exp ( 1 4 | T A e i θ T B e i θ | 2 N ) .
p 2 ( zero | θ ) = exp [ η sin 2 ( θ ) N ] .
P dark ( n ) = e r r n n ! .
p 3 ( zero | θ ) = p ( zero | θ ) P dark ( 0 ) = exp [ sin 2 ( θ ) N r ] .
p 4 ( zero | θ ) = exp [ sin 2 ( θ ) N e r ] ,
p ( θ | W ) = 1 G k = 1 M p ( W k | θ ) ,
G = π π k = 1 M p ( W k | θ ) d θ .
p ( θ | θ * ) = 1 G exp [ M p ( nonzero | θ * ) log p ( nonzero | θ ) + M p ( zero | θ * ) log p ( zero | θ ) ] ,
p ( zero | θ ) = 0.911 exp { 4.11 sin 2 [ 2 ( θ + 0.686 ) ] } .
p ( zero | θ ) = exp { 4.11 sin 2 [ 2 ( θ + 0.686 ) ] n b } ,

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