Abstract

We report on an orbital-angular-momentum-enhanced scheme for angular displacement estimation based on two-mode squeezed vacuum and parity detection. The sub-Heisenberg-limited sensitivity for angular displacement estimation is obtained in an ideal situation. Several realistic factors are also considered, including photon loss, dark counts, response-time delay, and thermal photon noise. Our results indicate that the effects of realistic factors on the sensitivity can be offset by raising orbital angular momentum quantum number . This implies that the robustness and the practicability of the system can be improved via raising without changing mean photon number N.

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

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References

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  1. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
    [Crossref] [PubMed]
  2. V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011).
    [Crossref]
  3. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science. 306, 1330–1336 (2004).
    [Crossref] [PubMed]
  4. B. C. Barish and R. Weiss, “LIGO and the detection of gravitational waves,” Phys. Today 52, 44 (1999).
    [Crossref]
  5. R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.  1, 121 (2010).
    [Crossref] [PubMed]
  6. P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
    [Crossref] [PubMed]
  7. T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
    [Crossref] [PubMed]
  8. Y. Israel, R. Tenne, O. Dan, and Y. Silberberg, “Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera,” Nat. Commun.  8, 14786 (2017).
    [Crossref] [PubMed]
  9. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733 (2000).
    [Crossref] [PubMed]
  10. J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
    [Crossref]
  11. A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
    [Crossref]
  12. J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
    [Crossref]
  13. 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]
  14. L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
    [Crossref]
  15. 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. 4, 2432 (2013).
  16. M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry,” Phys. Rev. A 90, 025802 (2014).
    [Crossref]
  17. 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]
  18. C. C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).
    [Crossref]
  19. C. C. Gerry, A. Benmoussa, and R. Campos, “Quantum nondemolition measurement of parity and generation of parity eigenstates in optical fields,” Phys. Rev. A 72, 053818 (2005).
    [Crossref]
  20. J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
    [Crossref]
  21. L. Cohen, D. Istrati, L. Dovrat, and H. Eisenberg, “Super-resolved phase measurements at the shot noise limit by parity measurement,” Opt. Express 22, 11945–11953 (2014).
    [Crossref] [PubMed]
  22. W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys.  12, 113025 (2010).
    [Crossref]
  23. 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]
  24. C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys.  84, 621 (2012).
    [Crossref]
  25. X. Ma, C. You, S. Adhikari, E. S. Matekole, H. Lee, and J. P. Dowling, “Sub-shot-noise-limited phase estimation via SU(1, 1) interferometer with thermal states,” https://arXiv:1711.03635 (2017).
  26. J. P. Dowling, “Quantum optical metrology–the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008).
    [Crossref]
  27. M. Chekhova and Z. Ou, “Nonlinear interferometers in quantum optics,” Adv. Opt. Photon. 8, 104–155 (2016).
    [Crossref]
  28. T. Ono and H. F. Hofmann, “Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum,” Phys. Rev. A 81, 033819 (2010).
    [Crossref]
  29. 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]

2017 (5)

Y. Israel, R. Tenne, O. Dan, and Y. Silberberg, “Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera,” Nat. Commun.  8, 14786 (2017).
[Crossref] [PubMed]

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (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]

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)

2014 (3)

L. Cohen, D. Istrati, L. Dovrat, and H. Eisenberg, “Super-resolved phase measurements at the shot noise limit by parity measurement,” Opt. Express 22, 11945–11953 (2014).
[Crossref] [PubMed]

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]

M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry,” Phys. Rev. A 90, 025802 (2014).
[Crossref]

2013 (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. 4, 2432 (2013).

2012 (1)

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys.  84, 621 (2012).
[Crossref]

2011 (2)

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011).
[Crossref]

2010 (5)

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.  1, 121 (2010).
[Crossref] [PubMed]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys.  12, 113025 (2010).
[Crossref]

T. Ono and H. F. Hofmann, “Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum,” Phys. Rev. A 81, 033819 (2010).
[Crossref]

2009 (1)

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
[Crossref]

2008 (1)

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

2006 (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

2005 (1)

C. C. Gerry, A. Benmoussa, and R. Campos, “Quantum nondemolition measurement of parity and generation of parity eigenstates in optical fields,” Phys. Rev. A 72, 053818 (2005).
[Crossref]

2004 (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science. 306, 1330–1336 (2004).
[Crossref] [PubMed]

2000 (2)

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733 (2000).
[Crossref] [PubMed]

C. C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).
[Crossref]

1999 (1)

B. C. Barish and R. Weiss, “LIGO and the detection of gravitational waves,” Phys. Today 52, 44 (1999).
[Crossref]

1998 (1)

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (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]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733 (2000).
[Crossref] [PubMed]

Adhikari, S.

X. Ma, C. You, S. Adhikari, E. S. Matekole, H. Lee, and J. P. Dowling, “Sub-shot-noise-limited phase estimation via SU(1, 1) interferometer with thermal states,” https://arXiv:1711.03635 (2017).

Agarwal, G. S.

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
[Crossref]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys.  12, 113025 (2010).
[Crossref]

Allen, L.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

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]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys.  12, 113025 (2010).
[Crossref]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

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. 4, 2432 (2013).

Barish, B. C.

B. C. Barish and R. Weiss, “LIGO and the detection of gravitational waves,” Phys. Today 52, 44 (1999).
[Crossref]

Bauchrowitz, J.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Benmoussa, A.

C. C. Gerry, A. Benmoussa, and R. Campos, “Quantum nondemolition measurement of parity and generation of parity eigenstates in optical fields,” Phys. Rev. A 72, 053818 (2005).
[Crossref]

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]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733 (2000).
[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]

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
[Crossref]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733 (2000).
[Crossref] [PubMed]

Campos, R.

C. C. Gerry, A. Benmoussa, and R. Campos, “Quantum nondemolition measurement of parity and generation of parity eigenstates in optical fields,” Phys. Rev. A 72, 053818 (2005).
[Crossref]

Caves, C. M.

M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry,” Phys. Rev. A 90, 025802 (2014).
[Crossref]

Cen, L.

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

Cerf, N. J.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys.  84, 621 (2012).
[Crossref]

Chekhova, M.

Chiruvelli, A.

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

Cohen, L.

Coldenstrodt-Ronge, H.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
[Crossref]

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]

Courtial, J.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[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. 4, 2432 (2013).

Dan, O.

Y. Israel, R. Tenne, O. Dan, and Y. Silberberg, “Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera,” Nat. Commun.  8, 14786 (2017).
[Crossref] [PubMed]

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. 4, 2432 (2013).

Dholakia, K.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

Dovrat, L.

Dowling, J. P.

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]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys.  12, 113025 (2010).
[Crossref]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

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

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733 (2000).
[Crossref] [PubMed]

X. Ma, C. You, S. Adhikari, E. S. Matekole, H. Lee, and J. P. Dowling, “Sub-shot-noise-limited phase estimation via SU(1, 1) interferometer with thermal states,” https://arXiv:1711.03635 (2017).

Eberle, T.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Eisenberg, H.

Eisert, J.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
[Crossref]

Feito, A.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
[Crossref]

Gao, H.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

García-Patrón, R.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys.  84, 621 (2012).
[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, A. Benmoussa, and R. Campos, “Quantum nondemolition measurement of parity and generation of parity eigenstates in optical fields,” Phys. Rev. A 72, 053818 (2005).
[Crossref]

C. C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).
[Crossref]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science. 306, 1330–1336 (2004).
[Crossref] [PubMed]

Händchen, V.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

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]

Hofmann, H. F.

T. Ono and H. F. Hofmann, “Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum,” Phys. Rev. A 81, 033819 (2010).
[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]

Huver, S. D.

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

Israel, Y.

Y. Israel, R. Tenne, O. Dan, and Y. Silberberg, “Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera,” Nat. Commun.  8, 14786 (2017).
[Crossref] [PubMed]

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]

Jha, A. K.

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
[Crossref]

Kok, P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733 (2000).
[Crossref] [PubMed]

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. 4, 2432 (2013).

Lam, P. K.

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.  1, 121 (2010).
[Crossref] [PubMed]

Lang, M. D.

M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry,” Phys. Rev. A 90, 025802 (2014).
[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]

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys.  12, 113025 (2010).
[Crossref]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

X. Ma, C. You, S. Adhikari, E. S. Matekole, H. Lee, and J. P. Dowling, “Sub-shot-noise-limited phase estimation via SU(1, 1) interferometer with thermal states,” https://arXiv:1711.03635 (2017).

Li, F.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

Li, S.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

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. 4, 2432 (2013).

Liu, J.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

Liu, W.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

Lloyd, S.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys.  84, 621 (2012).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science. 306, 1330–1336 (2004).
[Crossref] [PubMed]

Lundeen, J.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
[Crossref]

Ma, X.

X. Ma, C. You, S. Adhikari, E. S. Matekole, H. Lee, and J. P. Dowling, “Sub-shot-noise-limited phase estimation via SU(1, 1) interferometer with thermal states,” https://arXiv:1711.03635 (2017).

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011).
[Crossref]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science. 306, 1330–1336 (2004).
[Crossref] [PubMed]

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. 4, 2432 (2013).

Matekole, E. S.

X. Ma, C. You, S. Adhikari, E. S. Matekole, H. Lee, and J. P. Dowling, “Sub-shot-noise-limited phase estimation via SU(1, 1) interferometer with thermal states,” https://arXiv:1711.03635 (2017).

Mavalvala, N.

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.  1, 121 (2010).
[Crossref] [PubMed]

McClelland, D. E.

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.  1, 121 (2010).
[Crossref] [PubMed]

Mehmet, M.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[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]

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]

Müller-Ebhardt, H.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Ono, T.

T. Ono and H. F. Hofmann, “Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum,” Phys. Rev. A 81, 033819 (2010).
[Crossref]

Ou, Z.

Padgett, M. J.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

Pirandola, S.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys.  84, 621 (2012).
[Crossref]

Plenio, M.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
[Crossref]

Plick, W. N.

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys.  12, 113025 (2010).
[Crossref]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

Pregnell, K.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
[Crossref]

Ralph, T.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
[Crossref]

Ralph, T. C.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys.  84, 621 (2012).
[Crossref]

Raterman, G. M.

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

Robertson, D. A.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

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]

Schnabel, R.

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.  1, 121 (2010).
[Crossref] [PubMed]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[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. 4, 2432 (2013).

Shapiro, J. H.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys.  84, 621 (2012).
[Crossref]

Silberberg, Y.

Y. Israel, R. Tenne, O. Dan, and Y. Silberberg, “Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera,” Nat. Commun.  8, 14786 (2017).
[Crossref] [PubMed]

Silberhorn, C.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
[Crossref]

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]

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. 4, 2432 (2013).

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. 4, 2432 (2013).

Steinlechner, S.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Sun, Y.

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

Tenne, R.

Y. Israel, R. Tenne, O. Dan, and Y. Silberberg, “Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera,” Nat. Commun.  8, 14786 (2017).
[Crossref] [PubMed]

Vahlbruch, H.

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[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. 4, 2432 (2013).

Walmsley, I.

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
[Crossref]

Wang, F.

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

Weedbrook, C.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys.  84, 621 (2012).
[Crossref]

Wei, D.

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

Weiss, R.

B. C. Barish and R. Weiss, “LIGO and the detection of gravitational waves,” Phys. Today 52, 44 (1999).
[Crossref]

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733 (2000).
[Crossref] [PubMed]

Wineland, D. 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]

Yan, L.

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

You, C.

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]

X. Ma, C. You, S. Adhikari, E. S. Matekole, H. Lee, and J. P. Dowling, “Sub-shot-noise-limited phase estimation via SU(1, 1) interferometer with thermal states,” https://arXiv:1711.03635 (2017).

Zhang, J.

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

Zhang, Z.

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

Zhao, Y.

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

Adv. Opt. Photon. (1)

Contemp. Phys. (1)

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

EPJ Quantum Technol (1)

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]

Nat. Commun (2)

R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.  1, 121 (2010).
[Crossref] [PubMed]

Y. Israel, R. Tenne, O. Dan, and Y. Silberberg, “Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera,” Nat. Commun.  8, 14786 (2017).
[Crossref] [PubMed]

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. 4, 2432 (2013).

Nat. Photon. (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011).
[Crossref]

Nat. Phys. (1)

J. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. Pregnell, C. Silberhorn, T. Ralph, J. Eisert, M. Plenio, and I. Walmsley, “Tomography of quantum detectors,” Nat. Phys. 5, 27–30 (2009).
[Crossref]

New J. Phys (1)

W. N. Plick, P. M. Anisimov, J. P. Dowling, H. Lee, and G. S. Agarwal, “Parity detection in quantum optical metrology without number-resolving detectors,” New J. Phys.  12, 113025 (2010).
[Crossref]

Opt. Express (1)

Photonics Res. (1)

J. Liu, W. Liu, S. Li, D. Wei, H. Gao, and F. Li, “Enhancement of the angular rotation measurement sensitivity based on SU(2) and SU(1, 1) interferometers,” Photonics Res. 5, 617–622 (2017).
[Crossref]

Phys. Rev. A (8)

A. K. Jha, G. S. Agarwal, and R. W. Boyd, “Supersensitive measurement of angular displacements using entangled photons,” Phys. Rev. A 83, 053829 (2011).
[Crossref]

M. D. Lang and C. M. Caves, “Optimal quantum-enhanced interferometry,” Phys. Rev. A 90, 025802 (2014).
[Crossref]

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]

C. C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).
[Crossref]

C. C. Gerry, A. Benmoussa, and R. Campos, “Quantum nondemolition measurement of parity and generation of parity eigenstates in optical fields,” Phys. Rev. A 72, 053818 (2005).
[Crossref]

L. Cen, Z. Zhang, J. Zhang, S. Li, Y. Sun, L. Yan, Y. Zhao, and F. Wang, “State preparation and detector effects in quantum measurements of rotation with circular polarization-entangled photons and photon counting,” Phys. Rev. A 96, 053846 (2017).
[Crossref]

T. Ono and H. F. Hofmann, “Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum,” Phys. Rev. A 81, 033819 (2010).
[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]

Phys. Rev. Lett. (6)

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[Crossref]

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]

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
[Crossref] [PubMed]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733 (2000).
[Crossref] [PubMed]

P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, “Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit,” Phys. Rev. Lett. 104, 103602 (2010).
[Crossref] [PubMed]

T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection,” Phys. Rev. Lett. 104, 251102 (2010).
[Crossref] [PubMed]

Phys. Today (1)

B. C. Barish and R. Weiss, “LIGO and the detection of gravitational waves,” Phys. Today 52, 44 (1999).
[Crossref]

Rev. Mod. Phys (1)

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys.  84, 621 (2012).
[Crossref]

Science. (1)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: beating the standard quantum limit,” Science. 306, 1330–1336 (2004).
[Crossref] [PubMed]

Other (1)

X. Ma, C. You, S. Adhikari, E. S. Matekole, H. Lee, and J. P. Dowling, “Sub-shot-noise-limited phase estimation via SU(1, 1) interferometer with thermal states,” https://arXiv:1711.03635 (2017).

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Figures (5)

Fig. 1
Fig. 1 Schematic of proposed OAM-enhanced angular displacement estimation. The TMSV state is produced by an OPA and enters the SU(2) interferometer combined with two sets of SPPs and DPs. Parity measurement is carried out in the output. OPA, optical parametric amplifier; M, mirror; BS, beam splitter; SPP, spiral phase plate; DP, Dove prism; PNRD, photon-number-resolving detector; SP, signal processor.
Fig. 2
Fig. 2 (a) Sensitivity with angular displacement and different photon loss values in the case of = 1 and r = 1. (b) Optimal sensitivity of TMSV state with parity detection in the case of = 1 and photon loss. The losses are L = 1% and L = 3%. The value range of squeezing factor r changes from 0.5 to 1.5.
Fig. 3
Fig. 3 (a) Sensitivity with angular displacement, dark counts and response-time delay in the case of = 1 and r = 1. The rate of dark counts d = 0.01 and d = 0.1 model the case of only dark counts and response-time delay combined with dark counts, respectively. (b) Optimal sensitivity of TMSV state with parity detection in the case of = 1 and dark counts. The value range of squeezing factor r changes from 0.5 to 1.5.
Fig. 4
Fig. 4 (a) Sensitivity with angular displacement and thermal photon noise nth = 0.1 in the case of = 1 and r = 1. The transmissivities are T = 99% and T = 97%. (b) Optimal sensitivity of TMSV state with parity detection in the case of = 1 and nth = 0.1. The value range of squeezing factor r changes from 0.5 to 1.5.
Fig. 5
Fig. 5 Optimal sensitivity of TMSV state with parity detection in the case of L = 1% and different quantum numbers.

Equations (40)

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| ψ in = m = 0 ( 1 t ) t m | m , m ,
W ( X ) = exp [ ( X M ) Γ 1 ( X M ) ] π k det ( Γ ) ,
W ( x 1 , p 1 , x 2 , p 2 ) = 1 π 2 exp [ 2 ( p 1 p 2 x 1 , x 2 ) sinh 2 r ( x 1 2 + x 2 2 + p 1 2 + p 2 2 ) cosh 2 r ] ,
X out = S X in ,
Π ^ = π W out ( 0 , 0 ) .
Γ in = ( cosh ( 2 r ) I 2 sinh ( 2 r ) Z 2 sinh ( 2 r ) Z 2 cosh ( 2 r ) I 2 ) 4 × 4 ,
M out = S M in ,
Γ out = S Γ in S .
Π ^ B = exp ( M out ( 3 , 4 ) Γ out ( 3 , 4 ) 1 M out ( 3 , 4 ) ) | Γ out ( 3 , 4 ) | = 1 1 + N ( N + 2 ) cos 2 ( 2 φ ) ,
V = Π ^ B max Π ^ B min Π ^ B max + Π ^ B min
Δ φ = 1 1 / R 1 | R 2 / R 1 3 2 | ,
R 1 = 1 + N ( N + 2 ) cos 2 ( 2 φ ) ,
R 2 = N ( N + 2 ) sin ( 4 φ ) .
Δ φ min = 1 2 N ( N + 2 ) .
Π ^ B PL = 1 K 1 ,
Δ φ PL = 1 1 / K 1 | K 2 / K 1 3 2 | ,
K 1 = 1 + 1 2 ( 1 L ) 2 { N ( N + 2 ) cos ( 4 φ ) + N 2 } + ( 1 L 2 ) N ,
K 2 = ( 1 L ) 2 N ( N + 2 ) sin ( 4 φ ) .
lim N 1 N ( N + 2 ) 1 N ,
Π ^ B DC = e 2 d Π ^ B ,
Δ φ DC = 1 e 4 d / R 1 e 2 d | R 2 / R 1 3 2 | ,
Π ^ B TN = 1 H 1 ,
Δ φ TN = 1 1 / H 1 | H 2 / H 1 3 2 | ,
H 1 = T 2 4 { 2 cos 2 ( 2 φ ) [ 2 N ( N + 2 ) + 1 ] cos ( 4 φ ) + 7 } + 1 + 4 ( n th 2 + n th ) ( 1 T ) 2 2 T + 2 ( 2 n th + 1 ) ( 1 T ) ( N + 1 ) ,
H 2 = T 2 sin ( 4 φ ) N ( N + 2 ) .
S BS 1 = S BS 2 = 1 2 ( I 2 I 2 I 2 I 2 ) 4 × 4 ,
S AD = ( Θ 2 O 2 O 2 I 2 ) 4 × 4 ,
Θ 2 = ( cos ( 2 φ ) sin ( 2 φ ) sin ( 2 φ ) cos ( 2 φ ) ) .
Γ th = ( 2 n th + 1 ) I 2 .
γ 11 = γ 33 = cosh ( 2 r ) sin 2 ( 2 φ ) sinh ( 2 r ) ,
γ 22 = γ 44 = cosh ( 2 r ) + sin 2 ( 2 φ ) sinh ( 2 r ) ,
γ 12 = γ 21 = γ 14 = γ 41 = γ 23 = γ 32 = γ 34 = γ 43 = 1 2 sin ( 4 φ ) sinh ( 2 r ) ,
γ 13 = γ 31 = cos 2 ( 2 φ ) sinh ( 2 r ) ,
γ 24 = γ 42 = cos 2 ( 2 φ ) sinh ( 2 r ) .
Γ in * = ( Γ in O 4 O 4 Γ th Γ th , ) 8 × 8 ,
S BS 1 * = S BS 2 * = ( S BS O 4 O 4 I 4 ) 8 × 8 ,
S AD * = ( S AD O 4 O 4 I 4 ) 8 × 8 ,
S VBS * = ( T I 4 1 T I 4 1 T I 4 T I 4 ) 8 × 8 ,
Γ out * = S * Γ in * ( S * ) ,
M in * = ( M in M th ) .