Abstract

Quantum metrology allows for a tremendous boost in the accuracy of measurement of diverse physical parameters. The estimation of a rotation constitutes a remarkable example of this quantum-enhanced precision. The recently introduced Kings of Quantumness are especially germane for this task when the rotation axis is unknown, as they have a sensitivity independent of that axis and they achieve a Heisenberg-limit scaling. Here, we report the experimental realization of these states by generating up to 21-dimensional orbital angular momentum states of single photons, and confirm their high metrological abilities.

© 2017 Optical Society of America

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References

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    [Crossref]
  2. A. Perelomov, Generalized Coherent States and Their Applications (Springer, 1986).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  7. W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, Phys. Rev. Lett. 104, 133601 (2010).
    [Crossref]
  8. R. J. Sewell, M. Koschorreck, M. Napolitano, B. Dubost, N. Behbood, and M. W. Mitchell, Phys. Rev. Lett. 109, 253605 (2012).
    [Crossref]
  9. W. Muessel, H. Strobel, D. Linnemann, D. B. Hume, and M. K. Oberthaler, Phys. Rev. Lett. 113, 103004 (2014).
    [Crossref]
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    [Crossref]
  11. 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, Nat. Commun. 4, 2432 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref]
  15. A. Luis and L. L. Sánchez-Soto, Prog. Opt. 41, 421 (2000).
    [Crossref]
  16. K. Blum, Density Matrix Theory and Applications (Plenum, 1981).
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    [Crossref]
  18. L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).
  19. D. S. Simon, G. Jaeger, and A. V. Sergienko, Quantum Metrology, Imaging, and Communication (Springer, 2017).
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    [Crossref]
  21. E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, Opt. Lett. 38, 3546 (2013).
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    [Crossref]
  23. A. Baecklund and I. Bengtsson, Phys. Scripta T163, 014012 (2014).
    [Crossref]
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  25. O. Giraud, P. Braun, and D. Braun, New J. Phys. 12, 063005 (2010).
    [Crossref]
  26. J. J. Thomson, Philos. Mag. 7(39), 237 (1904).
    [Crossref]

2015 (2)

G. Björk, A. B. Klimov, P. de la Hoz, M. Grassl, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 92, 031801 (2015).
[Crossref]

G. Björk, M. Grassl, P. de la Hoz, G. Leuchs, and L. L. Sánchez-Soto, Phys. Scripta 90, 108008 (2015).
[Crossref]

2014 (4)

W. Muessel, H. Strobel, D. Linnemann, D. B. Hume, and M. K. Oberthaler, Phys. Rev. Lett. 113, 103004 (2014).
[Crossref]

L. A. Rozema, D. H. Mahler, R. Blume-Kohout, and A. M. Steinberg, Phys. Rev. X 4, 041025 (2014).
[Crossref]

A. Baecklund and I. Bengtsson, Phys. Scripta T163, 014012 (2014).
[Crossref]

H. Qassim, F. M. Miatto, J. P. Torres, M. J. Padgett, E. Karimi, and R. W. Boyd, J. Opt. Soc. Am. B 31, A20 (2014).
[Crossref]

2013 (3)

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, Nat. Commun. 4, 2432 (2013).
[Crossref]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, Opt. Lett. 38, 3546 (2013).
[Crossref]

P. de la Hoz, A. B. Klimov, G. Björk, Y. H. Kim, C. Müller, C. Marquardt, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 88, 063803 (2013).
[Crossref]

2012 (1)

R. J. Sewell, M. Koschorreck, M. Napolitano, B. Dubost, N. Behbood, and M. W. Mitchell, Phys. Rev. Lett. 109, 253605 (2012).
[Crossref]

2011 (1)

V. Giovannetti, S. Lloyd, and L. Maccone, Nat. Photonics 5, 222 (2011).
[Crossref]

2010 (2)

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, Phys. Rev. Lett. 104, 133601 (2010).
[Crossref]

O. Giraud, P. Braun, and D. Braun, New J. Phys. 12, 063005 (2010).
[Crossref]

2008 (1)

P. Kolenderski and R. Demkowicz-Dobrzanski, Phys. Rev. A 78, 052333 (2008).
[Crossref]

2006 (2)

S. Chaturvedi, G. Marmo, and N. Mukunda, Rev. Math. Phys. 18, 887 (2006).
[Crossref]

J. Zimba, Electron. J. Theor. Phys. 3, 143 (2006).

2002 (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

2001 (1)

V. Meyer, M. A. Rowe, D. Kielpinski, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Phys. Rev. Lett. 86, 5870 (2001).
[Crossref]

2000 (1)

A. Luis and L. L. Sánchez-Soto, Prog. Opt. 41, 421 (2000).
[Crossref]

1963 (1)

R. J. Glauber, Phys. Rev. 131, 2766 (1963).
[Crossref]

1932 (1)

E. Majorana, Nuovo Cimento 9, 43 (1932).
[Crossref]

1904 (1)

J. J. Thomson, Philos. Mag. 7(39), 237 (1904).
[Crossref]

Allen, L.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).

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, Nat. Commun. 4, 2432 (2013).
[Crossref]

Baecklund, A.

A. Baecklund and I. Bengtsson, Phys. Scripta T163, 014012 (2014).
[Crossref]

Balabas, M. V.

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, Phys. Rev. Lett. 104, 133601 (2010).
[Crossref]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).

Behbood, N.

R. J. Sewell, M. Koschorreck, M. Napolitano, B. Dubost, N. Behbood, and M. W. Mitchell, Phys. Rev. Lett. 109, 253605 (2012).
[Crossref]

Bengtsson, I.

A. Baecklund and I. Bengtsson, Phys. Scripta T163, 014012 (2014).
[Crossref]

Bent, N.

Björk, G.

G. Björk, A. B. Klimov, P. de la Hoz, M. Grassl, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 92, 031801 (2015).
[Crossref]

G. Björk, M. Grassl, P. de la Hoz, G. Leuchs, and L. L. Sánchez-Soto, Phys. Scripta 90, 108008 (2015).
[Crossref]

P. de la Hoz, A. B. Klimov, G. Björk, Y. H. Kim, C. Müller, C. Marquardt, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 88, 063803 (2013).
[Crossref]

Blum, K.

K. Blum, Density Matrix Theory and Applications (Plenum, 1981).

Blume-Kohout, R.

L. A. Rozema, D. H. Mahler, R. Blume-Kohout, and A. M. Steinberg, Phys. Rev. X 4, 041025 (2014).
[Crossref]

Bolduc, E.

Boyd, R. W.

Braun, D.

O. Giraud, P. Braun, and D. Braun, New J. Phys. 12, 063005 (2010).
[Crossref]

Braun, P.

O. Giraud, P. Braun, and D. Braun, New J. Phys. 12, 063005 (2010).
[Crossref]

Chaturvedi, S.

S. Chaturvedi, G. Marmo, and N. Mukunda, Rev. Math. Phys. 18, 887 (2006).
[Crossref]

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[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, Nat. Commun. 4, 2432 (2013).
[Crossref]

de la Hoz, P.

G. Björk, A. B. Klimov, P. de la Hoz, M. Grassl, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 92, 031801 (2015).
[Crossref]

G. Björk, M. Grassl, P. de la Hoz, G. Leuchs, and L. L. Sánchez-Soto, Phys. Scripta 90, 108008 (2015).
[Crossref]

P. de la Hoz, A. B. Klimov, G. Björk, Y. H. Kim, C. Müller, C. Marquardt, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 88, 063803 (2013).
[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, Nat. Commun. 4, 2432 (2013).
[Crossref]

Demkowicz-Dobrzanski, R.

P. Kolenderski and R. Demkowicz-Dobrzanski, Phys. Rev. A 78, 052333 (2008).
[Crossref]

Dubost, B.

R. J. Sewell, M. Koschorreck, M. Napolitano, B. Dubost, N. Behbood, and M. W. Mitchell, Phys. Rev. Lett. 109, 253605 (2012).
[Crossref]

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, Nat. Photonics 5, 222 (2011).
[Crossref]

Giraud, O.

O. Giraud, P. Braun, and D. Braun, New J. Phys. 12, 063005 (2010).
[Crossref]

Glauber, R. J.

R. J. Glauber, Phys. Rev. 131, 2766 (1963).
[Crossref]

Grassl, M.

G. Björk, A. B. Klimov, P. de la Hoz, M. Grassl, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 92, 031801 (2015).
[Crossref]

G. Björk, M. Grassl, P. de la Hoz, G. Leuchs, and L. L. Sánchez-Soto, Phys. Scripta 90, 108008 (2015).
[Crossref]

Hume, D. B.

W. Muessel, H. Strobel, D. Linnemann, D. B. Hume, and M. K. Oberthaler, Phys. Rev. Lett. 113, 103004 (2014).
[Crossref]

Itano, W. M.

V. Meyer, M. A. Rowe, D. Kielpinski, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Phys. Rev. Lett. 86, 5870 (2001).
[Crossref]

Jaeger, G.

D. S. Simon, G. Jaeger, and A. V. Sergienko, Quantum Metrology, Imaging, and Communication (Springer, 2017).

Jensen, K.

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, Phys. Rev. Lett. 104, 133601 (2010).
[Crossref]

Karimi, E.

Kielpinski, D.

V. Meyer, M. A. Rowe, D. Kielpinski, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Phys. Rev. Lett. 86, 5870 (2001).
[Crossref]

Kim, Y. H.

P. de la Hoz, A. B. Klimov, G. Björk, Y. H. Kim, C. Müller, C. Marquardt, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 88, 063803 (2013).
[Crossref]

Klimov, A. B.

G. Björk, A. B. Klimov, P. de la Hoz, M. Grassl, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 92, 031801 (2015).
[Crossref]

P. de la Hoz, A. B. Klimov, G. Björk, Y. H. Kim, C. Müller, C. Marquardt, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 88, 063803 (2013).
[Crossref]

Kolenderski, P.

P. Kolenderski and R. Demkowicz-Dobrzanski, Phys. Rev. A 78, 052333 (2008).
[Crossref]

Koschorreck, M.

R. J. Sewell, M. Koschorreck, M. Napolitano, B. Dubost, N. Behbood, and M. W. Mitchell, Phys. Rev. Lett. 109, 253605 (2012).
[Crossref]

Krauter, H.

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, Phys. Rev. Lett. 104, 133601 (2010).
[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, Nat. Commun. 4, 2432 (2013).
[Crossref]

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

Leuchs, G.

G. Björk, A. B. Klimov, P. de la Hoz, M. Grassl, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 92, 031801 (2015).
[Crossref]

G. Björk, M. Grassl, P. de la Hoz, G. Leuchs, and L. L. Sánchez-Soto, Phys. Scripta 90, 108008 (2015).
[Crossref]

P. de la Hoz, A. B. Klimov, G. Björk, Y. H. Kim, C. Müller, C. Marquardt, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 88, 063803 (2013).
[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, Nat. Commun. 4, 2432 (2013).
[Crossref]

Linnemann, D.

W. Muessel, H. Strobel, D. Linnemann, D. B. Hume, and M. K. Oberthaler, Phys. Rev. Lett. 113, 103004 (2014).
[Crossref]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, Nat. Photonics 5, 222 (2011).
[Crossref]

Luis, A.

A. Luis and L. L. Sánchez-Soto, Prog. Opt. 41, 421 (2000).
[Crossref]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, Nat. Photonics 5, 222 (2011).
[Crossref]

Mahler, D. H.

L. A. Rozema, D. H. Mahler, R. Blume-Kohout, and A. M. Steinberg, Phys. Rev. X 4, 041025 (2014).
[Crossref]

Majorana, E.

E. Majorana, Nuovo Cimento 9, 43 (1932).
[Crossref]

Marmo, G.

S. Chaturvedi, G. Marmo, and N. Mukunda, Rev. Math. Phys. 18, 887 (2006).
[Crossref]

Marquardt, C.

P. de la Hoz, A. B. Klimov, G. Björk, Y. H. Kim, C. Müller, C. Marquardt, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 88, 063803 (2013).
[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, Nat. Commun. 4, 2432 (2013).
[Crossref]

Meyer, V.

V. Meyer, M. A. Rowe, D. Kielpinski, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Phys. Rev. Lett. 86, 5870 (2001).
[Crossref]

Miatto, F. M.

Mitchell, M. W.

R. J. Sewell, M. Koschorreck, M. Napolitano, B. Dubost, N. Behbood, and M. W. Mitchell, Phys. Rev. Lett. 109, 253605 (2012).
[Crossref]

Monroe, C.

V. Meyer, M. A. Rowe, D. Kielpinski, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Phys. Rev. Lett. 86, 5870 (2001).
[Crossref]

Muessel, W.

W. Muessel, H. Strobel, D. Linnemann, D. B. Hume, and M. K. Oberthaler, Phys. Rev. Lett. 113, 103004 (2014).
[Crossref]

Mukunda, N.

S. Chaturvedi, G. Marmo, and N. Mukunda, Rev. Math. Phys. 18, 887 (2006).
[Crossref]

Müller, C.

P. de la Hoz, A. B. Klimov, G. Björk, Y. H. Kim, C. Müller, C. Marquardt, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 88, 063803 (2013).
[Crossref]

Napolitano, M.

R. J. Sewell, M. Koschorreck, M. Napolitano, B. Dubost, N. Behbood, and M. W. Mitchell, Phys. Rev. Lett. 109, 253605 (2012).
[Crossref]

Oberthaler, M. K.

W. Muessel, H. Strobel, D. Linnemann, D. B. Hume, and M. K. Oberthaler, Phys. Rev. Lett. 113, 103004 (2014).
[Crossref]

Padgett, M. J.

H. Qassim, F. M. Miatto, J. P. Torres, M. J. Padgett, E. Karimi, and R. W. Boyd, J. Opt. Soc. Am. B 31, A20 (2014).
[Crossref]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 88, 257901 (2002).
[Crossref]

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, 2003).

Perelomov, A.

A. Perelomov, Generalized Coherent States and Their Applications (Springer, 1986).

Polzik, E. S.

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, Phys. Rev. Lett. 104, 133601 (2010).
[Crossref]

Qassim, H.

Renema, J. J.

W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, Phys. Rev. Lett. 104, 133601 (2010).
[Crossref]

Rowe, M. A.

V. Meyer, M. A. Rowe, D. Kielpinski, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Phys. Rev. Lett. 86, 5870 (2001).
[Crossref]

Rozema, L. A.

L. A. Rozema, D. H. Mahler, R. Blume-Kohout, and A. M. Steinberg, Phys. Rev. X 4, 041025 (2014).
[Crossref]

Sackett, C. A.

V. Meyer, M. A. Rowe, D. Kielpinski, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Phys. Rev. Lett. 86, 5870 (2001).
[Crossref]

Sánchez-Soto, L. L.

G. Björk, M. Grassl, P. de la Hoz, G. Leuchs, and L. L. Sánchez-Soto, Phys. Scripta 90, 108008 (2015).
[Crossref]

G. Björk, A. B. Klimov, P. de la Hoz, M. Grassl, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 92, 031801 (2015).
[Crossref]

P. de la Hoz, A. B. Klimov, G. Björk, Y. H. Kim, C. Müller, C. Marquardt, G. Leuchs, and L. L. Sánchez-Soto, Phys. Rev. A 88, 063803 (2013).
[Crossref]

A. Luis and L. L. Sánchez-Soto, Prog. Opt. 41, 421 (2000).
[Crossref]

Santamato, E.

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, Nat. Commun. 4, 2432 (2013).
[Crossref]

Sergienko, A. V.

D. S. Simon, G. Jaeger, and A. V. Sergienko, Quantum Metrology, Imaging, and Communication (Springer, 2017).

Sewell, R. J.

R. J. Sewell, M. Koschorreck, M. Napolitano, B. Dubost, N. Behbood, and M. W. Mitchell, Phys. Rev. Lett. 109, 253605 (2012).
[Crossref]

Simon, D. S.

D. S. Simon, G. Jaeger, and A. V. Sergienko, Quantum Metrology, Imaging, and Communication (Springer, 2017).

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, Nat. Commun. 4, 2432 (2013).
[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, Nat. Commun. 4, 2432 (2013).
[Crossref]

Steinberg, A. M.

L. A. Rozema, D. H. Mahler, R. Blume-Kohout, and A. M. Steinberg, Phys. Rev. X 4, 041025 (2014).
[Crossref]

Strobel, H.

W. Muessel, H. Strobel, D. Linnemann, D. B. Hume, and M. K. Oberthaler, Phys. Rev. Lett. 113, 103004 (2014).
[Crossref]

Thomson, J. J.

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Supplementary Material (1)

NameDescription
» Supplement 1       Additional derivations

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Figures (4)

Fig. 1.
Fig. 1.

(a) The Majorana constellations in the Bloch sphere for the Kings (orange) and the NOON states (yellow) corresponding to spin S=3, 5, 6, and 10. (b) The Laguerre–Gauss representation of the same Kings and NOON states, shown in (a), where the azimuthal index corresponds to m in the Dicke basis. We consider the fundamental radial mode, i.e., p=0, where p is the radial index of the Laguerre–Gauss modes.

Fig. 2.
Fig. 2.

(a) Sketch of the experimental setup and (b) density plots of the experimentally reconstructed Husimi Q functions for the same King states as in Fig. 1. The fidelities of these reconstructed states are (from left to right) 0.94, 0.87, 0.91, and 0.93. The differences with the theoretical Q functions cannot be visually noticed.

Fig. 3.
Fig. 3.

Experimental results of the projection of the S=3, 6, and 10 (first, second, and third column, respectively) Kings states, |Ψ(S), onto themselves after a rotation of ω around the axis u, R^(ω,u), i.e., P^=|Ψ(S)|R^(ω,u)|Ψ(S)|2. The axes are presented graphically along with the associated constellations. The first row corresponds to rotations along the axes passing through the Majorana points (pink arrows), and the second row corresponds to rotations along the axes normal to the facets of the constellations (blue arrows). The experimental results (red and blue dots) are shown along with the theoretical results (blue and green curves) for all rotation axes.

Fig. 4.
Fig. 4.

Rotational sensitivity Δω for the Kings (red) and NOON states (blue). The solid curves correspond to the theory predicted in Eq. (1), and the points correspond to experimental results. In the case of the Kings, we show the mean rotational sensitivity over all axes presented in Fig. 3, where the error bars correspond to variation in sensitivity from axes to axes. For the NOON states, we show the rotational sensitivity for rotation axes with Θ=0 and Θ=π/2.

Equations (1)

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ΔωKings=321S(S+1),ΔωNOON=1212S2cos2Θ+Ssin2Θ.