Abstract

Visibility V and distinguishability D quantify wave-ray duality: V2+D21. We join them to polarization P via the Polarization Coherence Theorem, a tight equality: P2=V2+D2.

© 2017 Optical Society of America

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References

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  1. Th. Young, Philos. Trans. R. Soc. London 92, 12 (1802).
    [Crossref]
  2. J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
    [Crossref]
  3. T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
    [Crossref]
  4. A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
    [Crossref]
  5. X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
    [Crossref]
  6. An examination by W. K. Wootters and W. H. Zurek, in Phys. Rev. D19, 473 (1979) opened for discussion a quantification of complementarity that is available via the Young experiment, and almost uncountably many derivations and re-derivations related to the result V2+D2≤1 given in Eq. (5) have appeared since 1985: R. J. Glauber, Ann. New York Acad. Sci. 480, 336–372 (1986); D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988); L. Mandel, Opt. Lett. 16, 1882 (1991); G. Jaeger, M. A. Horne, and A. Shimony, Phys. Rev. A 48, 1023 (1993); G. Jaeger, A. Shimony, and L. Vaidman, Phys. Rev. A 51, 54 (1993); B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996); S. Dürr, T. Nonn, and G. Rempe, Phys. Rev. Lett. 81, 5705 (1998); B.-G. Englert, M. O. Scully, and H. Walther, J. Mod. Opt. 47, 2213 (2000); M. Lahiri, Phys. Rev. A 83, 045803 (2011); H.-Y. Liu, J.-H. Huang, J.-R. Gao, M. S. Zubairy, and S.-Y. Zhu, Phys. Rev. A 85, 022106 (2012); F. De Zela, Phys. Rev. A 89, 013845 (2014).
  7. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).
  8. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [Crossref]
  9. X.-F. Qian, private communication.

2016 (2)

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

2015 (1)

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

2014 (1)

T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

2003 (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[Crossref]

1802 (1)

Th. Young, Philos. Trans. R. Soc. London 92, 12 (1802).
[Crossref]

Adesso, G.

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

Al Qasimi, A.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Ali, H.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Alonso, M. A.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Baumgratz, T.

T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

Bera, M. N.

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

Cramer, M.

T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

Dhar, H. S.

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

Eberly, J. H.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

Gutiérrez-Cuevas, R.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Howell, J. C.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Little, B. J.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Maholtra, T.

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

Malhotra, T.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Plenio, M. B.

T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

Qian, X.-F.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

X.-F. Qian, private communication.

Singh, U.

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

Streltsov, A.

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

Vamivakas, A. N.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

Wolf, E.

E. Wolf, Phys. Lett. A 312, 263 (2003).
[Crossref]

Wootters, W. K.

An examination by W. K. Wootters and W. H. Zurek, in Phys. Rev. D19, 473 (1979) opened for discussion a quantification of complementarity that is available via the Young experiment, and almost uncountably many derivations and re-derivations related to the result V2+D2≤1 given in Eq. (5) have appeared since 1985: R. J. Glauber, Ann. New York Acad. Sci. 480, 336–372 (1986); D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988); L. Mandel, Opt. Lett. 16, 1882 (1991); G. Jaeger, M. A. Horne, and A. Shimony, Phys. Rev. A 48, 1023 (1993); G. Jaeger, A. Shimony, and L. Vaidman, Phys. Rev. A 51, 54 (1993); B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996); S. Dürr, T. Nonn, and G. Rempe, Phys. Rev. Lett. 81, 5705 (1998); B.-G. Englert, M. O. Scully, and H. Walther, J. Mod. Opt. 47, 2213 (2000); M. Lahiri, Phys. Rev. A 83, 045803 (2011); H.-Y. Liu, J.-H. Huang, J.-R. Gao, M. S. Zubairy, and S.-Y. Zhu, Phys. Rev. A 85, 022106 (2012); F. De Zela, Phys. Rev. A 89, 013845 (2014).

Young, Th.

Th. Young, Philos. Trans. R. Soc. London 92, 12 (1802).
[Crossref]

Zurek, W. H.

An examination by W. K. Wootters and W. H. Zurek, in Phys. Rev. D19, 473 (1979) opened for discussion a quantification of complementarity that is available via the Young experiment, and almost uncountably many derivations and re-derivations related to the result V2+D2≤1 given in Eq. (5) have appeared since 1985: R. J. Glauber, Ann. New York Acad. Sci. 480, 336–372 (1986); D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988); L. Mandel, Opt. Lett. 16, 1882 (1991); G. Jaeger, M. A. Horne, and A. Shimony, Phys. Rev. A 48, 1023 (1993); G. Jaeger, A. Shimony, and L. Vaidman, Phys. Rev. A 51, 54 (1993); B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996); S. Dürr, T. Nonn, and G. Rempe, Phys. Rev. Lett. 81, 5705 (1998); B.-G. Englert, M. O. Scully, and H. Walther, J. Mod. Opt. 47, 2213 (2000); M. Lahiri, Phys. Rev. A 83, 045803 (2011); H.-Y. Liu, J.-H. Huang, J.-R. Gao, M. S. Zubairy, and S.-Y. Zhu, Phys. Rev. A 85, 022106 (2012); F. De Zela, Phys. Rev. A 89, 013845 (2014).

Philos. Trans. R. Soc. London (1)

Th. Young, Philos. Trans. R. Soc. London 92, 12 (1802).
[Crossref]

Phys. Lett. A (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[Crossref]

Phys. Rev. Lett. (3)

T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

A. Streltsov, U. Singh, H. S. Dhar, M. N. Bera, and G. Adesso, Phys. Rev. Lett. 115, 020403 (2015).
[Crossref]

X.-F. Qian, T. Maholtra, A. N. Vamivakas, and J. H. Eberly, Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

Phys. Scripta (1)

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, Phys. Scripta 91, 063003 (2016).
[Crossref]

Other (3)

X.-F. Qian, private communication.

An examination by W. K. Wootters and W. H. Zurek, in Phys. Rev. D19, 473 (1979) opened for discussion a quantification of complementarity that is available via the Young experiment, and almost uncountably many derivations and re-derivations related to the result V2+D2≤1 given in Eq. (5) have appeared since 1985: R. J. Glauber, Ann. New York Acad. Sci. 480, 336–372 (1986); D. M. Greenberger and A. Yasin, Phys. Lett. A 128, 391 (1988); L. Mandel, Opt. Lett. 16, 1882 (1991); G. Jaeger, M. A. Horne, and A. Shimony, Phys. Rev. A 48, 1023 (1993); G. Jaeger, A. Shimony, and L. Vaidman, Phys. Rev. A 51, 54 (1993); B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996); S. Dürr, T. Nonn, and G. Rempe, Phys. Rev. Lett. 81, 5705 (1998); B.-G. Englert, M. O. Scully, and H. Walther, J. Mod. Opt. 47, 2213 (2000); M. Lahiri, Phys. Rev. A 83, 045803 (2011); H.-Y. Liu, J.-H. Huang, J.-R. Gao, M. S. Zubairy, and S.-Y. Zhu, Phys. Rev. A 85, 022106 (2012); F. De Zela, Phys. Rev. A 89, 013845 (2014).

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

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Figures (1)

Fig. 1.
Fig. 1.

Double-slit interference setup. Classical light fields emerge from slits a and b and combine on screen c.

Equations (12)

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

F(r,z)=ua(r,z)ϕa(q)+ub(r,z)ϕb(q).
Ic=Ia+Ib+2|ϕa*ϕb|cos[arg(ϕa*ϕb)],
VF=IcmaxIcminIcmax+Icmin=2|ϕa*ϕb|Ia+Ib,
DF=|IaIb|Ia+Ib.
VF2+DF21.
E=h^Eh+v^Ev.
WE=[Eh*EhEv*EhEh*EvEv*Ev],PE=14DetWE(Tr[WE])2.
WF=[ϕa*ϕaϕb*ϕaϕa*ϕbϕb*ϕb],PF=14DetWF(Tr[WF])2.
PF2=14IaIb|ϕa*ϕb|2(Ia+Ib)2=(IaIb)2+4|ϕa*ϕb|2(Ia+Ib)2=(IaIb)2(Ia+Ib)2+4|ϕa*ϕb|2(Ia+Ib)2,
PF2DF2+VF2.
Eh=uaHa+ubHb,andEv=uaVa+ubVb.
F=(s^·E)=(s^·h^)(uaHa+ubHb)+(s^·v^)(uaVa+ubVb)=ua[(s^·h^)Ha+(s^·v^)Va]+ub[(s^·h^)Hb+(s^·v^)Vb],