Abstract
We propose and analyse a modified ghost-interference experiment, and show that revealing the particle nature of a particle passing through a double-slit hides the wave nature of a spatially separated particle which it is entangled with. We derive a nonlocal duality relation, \({\mathcal D}_1^2 + {\mathcal V}_2^2 \le 1\), which connects the path distinguishability of one particle to the interference visibility of the other. It extends Bohr’s principle of complementarity to a nonlocal scenario. We also propose a ghost quantum eraser in which, erasing the which-path information of one particle brings back the interference fringes of the other.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs40509-015-0064-4/MediaObjects/40509_2015_64_Fig1_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs40509-015-0064-4/MediaObjects/40509_2015_64_Fig2_HTML.gif)
Similar content being viewed by others
References
Bohr, N.: The quantum postulate and the recent development of atomic theory. Nature (London) 121, 580–591 (1928)
Greenberger, D.M., Yasin, A.: Simultaneous wave and particle knowledge in a neutron interferometer. Phys. Lett. A 128, 391 (1988)
Englert, B.-G.: Fringe visibility and which-way information: an inequality. Phys. Rev. Lett. 77, 2154 (1996)
Strekalov, D.V., Sergienko, A.V., Klyshko, D.N., Shih, Y.H.: Observation of two-photon ghost interference and diffraction. Phys. Rev. Lett. 74, 3600 (1995)
D’Angelo, M., Kim, Y.-H., Kulik, S.P., Shih, Y.: Identifying entanglement using quantum ghost interference and imaging. Phys. Rev. Lett. 92, 233601 (2004)
Thanvanthri, S., Rubin, M.H.: Ghost interference with an optical parametric amplifier. Phys. Rev. A 70, 063811 (2004)
Zhai, Y.-H., Chen, X.-H., Zhang, D., Wu, L.-A.: Two-photon interference with true thermal light. Phys. Rev. A 72, 043805 (2005)
Jie, L., **g, C.: Lensless ghost diffraction with partially coherent sources: effects of the source size, transverse coherence, detector size and defocusing length. Chin. Phys. Lett. 28, 094203 (2011)
Kofler, J., Singh, M., Ebner, M., Keller, M., Kotyrba, M.: Einstein-Podolsky-Rosen correlations from colliding Bose-Einstein condensates A. Zeiling er. Phys. Rev. A 86, 032115 (2012)
Chingangbam, P., Qureshi, T.: Ghost interference and quantum erasure. Prog. Theor. Phys. 127, 383–392 (2012)
Ding, D.-S., Zhou, Z.-Y., Shi, B.-S., Zou, X.-B., Guo, G.-C.: Two-color ghost interference. AIP Adv. 2, 032177 (2012)
Shafaq, S., Qureshi, T.: Theoretical analysis of two-color ghost interference. Eur. Phys. J. D 68, 52 (2014)
Qureshi, T., Chingangbam, P., Shafaq, S.: Understanding ghost interference. ar**v:1406.0633 [quant-ph]
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)
Klyshko, D.N.: A simple method of preparing pure states of an optical field, of implementing the EinsteinPodolsky Rosen experiment, and of demonstrating the complementarity principle. Sov. Phys. Usp. 31, 74 (1988)
Walborn, S.P., Monken, C.H., Pádua, S., Souto Ribeiro, P.H.: Spatial correlations in parametric down-conversion. Phys. Rep. 495, 87–139 (2010)
Vaccaro, J.A.: Particle-wave duality: a dichotomy between symmetry and asymmetry. Proc. R. Soc. A. 468, 1065–1084 (2012)
Qureshi, T.: Understanding Popper’s experiment. Am. J. Phys. 73, 541–544 (2005)
Born, M., Wolf, E.: Principles of Optics, 7th edn. Cambridge University Press, Cambridge (2002)
Barbosa, G.A.: Quantum images in double-slit experiments with spontaneous down-conversion light. Phys. Rev. A 54, 4473 (1996)
Wang, L.J., Zou, X.Y., Mandel, L.: Induced coherence without induced emission. Phys. Rev. A 44, 4614 (1991)
Zou, X.Y., Wang, L.J., Mandel, L.: Induced coherence and indistinguishability in optical interference. Phys. Rev. Lett. 67, 318 (1991)
Ou, Z.Y., Wang, L.J., Mandel, L.: Vacuum effects on interference in two-photon down conversion. Phys. Rev. A 40, 1428 (1989)
Hong, C.K., Mandel, L.: Experimental realization of a localized one-photon state. Phys. Rev. Lett. 56, 58 (1986)
Jaynes, E.: In: Barut, A.O. (ed.) Foundations of radiation theory and quantum electrodynamics, p. 37. Plenum, New York (1980)
Scully, M.O., Englert, B.-G., Walther, H.: Quantum optical tests of complementarity. Nature (London) 351, 111 (1991)
Walborn, S.P., Terra, M.O.: Cunha, S. Pádua, C.H. Monken.: Double-slit quantum eraser. Phys. Rev. A 65, 033818 (2002)
Walborn, S.P., Terra Cunha, M.O., Pádua, S., Monken, C.H.: Quantum erasure. Am. Sci. 91, 336–343 (2003)
Kim, Y.-H., Yu, R., Kulik, S.P., Shih, Y.: Delayed ‘choice’ quantum eraser. Phys. Rev. Lett. 84, 1 (2000)
Scarcelli, G., Zhou, Y., Shih, Y.: Random delayed-choice quantum eraser via two-photon imaging. Eur. Phys. J. D 44, 167–173 (2007)
Peng, T., Chen, H., Shih, Y.: Delayed-choice quantum eraser with thermal light. Phys. Rev. Lett. 112, 180401 (2014)
Acknowledgments
M. A. Siddiqui thanks the University Grants Commission, India, for financial support. Authors thank an anonymous referee for suggesting changes which improved the clarity of the discussion.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Siddiqui, M.A., Qureshi, T. A nonlocal wave–particle duality. Quantum Stud.: Math. Found. 3, 115–122 (2016). https://doi.org/10.1007/s40509-015-0064-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40509-015-0064-4