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Observing the Completed Quantum Complementarity
October 23, 201812:00 pm – 1:00 pm (CDT)

Observing the Completed Quantum Complementarity


Xiaofeng Qian (The Institute of Optics, University of Rochester)



Mitchell Physics Building

College Station, Texas 77843-4242

Event Details

Wave and particle are two standard yet contradictory fundamental features of a quantum identity, such as a photon, an electron, etc. (see for example a review in [1]). The common qualitative recognition has been Bohr's 1928 complementarity principle [2] which accommodates both features and is usually known as wave-particle duality due to de Broglie [3]. According to de Broglie and Bohr, every quantum identity has both particle and wave properties, but the two are exclusive to each other and can't be observed simultaneously. In 1979 Wootters and Zurek [4] and their followers introduced quantitative measures of waveness and particleness and achieved the well known duality inequality, V2 + D2 ≤ 1 [5], connecting the continuously varying wave interference visibility V and particle distinguishability D. This suggests the intermediate coexistence of partial waveness and partial particleness advancing Bohr's original concept of only one extreme property at a time. Recently, it has been demonstrated that a non-zero classical optical field can display neither wave nor ray property while having maximum entanglement, which leads to an exact complementary identity V2 + D2 + C2 = 1 with concurrence C charactering entanglement [6]. This implies the need of a further completed complementarity also in the quantum regime. In this talk I will discuss our recent results that extend the three-way complementary identity relation to single quantum identities showing the coexistence of three fundamental features, i.e., wave, particle and entanglement. Experimental confirmation is also demonstrated using single photons generated by two-dimensional defect-hosted hexagonal Boron Nitride (hBN) quantum emitters. We observe explicitly the characteristic features of this three-way complementary relation, i.e., complete behavior of either one of the three features, coexistence of either two, and coexistence of all three. This covers and further extends the previous complementary wave-particle inequality. We display the results with a complementarity sphere.
- M. O. Scully, B.-G.Englert, and Herbert Walther, Quantum optical tests of complementarity, Nature 351, 111-116 (1991)
- N. Bohr, Naturwissenschaften 16, 245 (1928); Nature (London) 121, 580 (1928).
- L. de Broglie, Waves and Quanta, Nature (London) 112, 540 (1923); and Recherches sur la thorie des quanta, Annales de Physique, 10(3), 22-128 (1925)
- W. K. Wootters and W. H. Zurek, Phys. Rev. D 19, 473 (1979)
- D. M. Greenberger and A. Yasin Phys. Lett. A 128, 391 (1988); G. Jaeger, M. A. Horne, and A. Shimony Phys. Rev. A 48, 1023 (1993); B.G. Englert, Phys. Rev. Lett. 77, 2154 (1996)
- Xiao-Feng Qian, A.N. Vamivakas, and J.H. Eberly, Entanglement Limits Duality and Vice Versa, Optica 5, 942-947 (2018).

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