Quantum superposition is the cornerstone of quantum mechanics, where interference fringes originate in the self-interference of a single photon via indistinguishable photon characteristics. Wheeler’s delayed-choice experiments have been extensively studied for the wave-particle duality over the last several decades to understand the complementarity theory of quantum mechanics. The heart of the delayed-choice quantum eraser is in the mutually exclusive quantum feature violating the cause-effect relation. Here, we experimentally demonstrate the quantum eraser using coherent photon pairs by the delayed choice of a polarizer placed out of the interferometer. Coherence solutions of the observed quantum eraser are derived from a typical Mach–Zehnder interferometer, where the violation of the cause-effect relation is due to selective measurements of basis choice.
Quantum mechanics has been developed based on the wave-particle duality1 of a single particle over the last century, resulting in various quantum technologies in computing2,3,4, communications5,6,7, and sensing areas8,9,10. In a single photon’s self-interference11, quantum superposition between orthonormal bases of the single photon plays an essential role12,13,14,15. The wave-particle duality originated in quantum superposition must be exclusive in their natures according to the Copenhagen interpretation16,17,18. In that sense, the delayed-choice quantum eraser12,13,14,15,19 can be understood as an ad-hoc quantum superposition of a measured photon through a dynamic window of a polarizer19. Due to the exclusive nature of the wave-particle duality, the violation of the cause-effect relation in the quantum eraser can also be understood for the superposition of many waves resulting in the bandwidth-limited effective coherence, where no quantum feature exists beyond the ensemble coherence19.
Quantum entanglement is between two or more individual photons (particles) whose presumably assumed fixed phase relation between paired photons does not violate quantum mechanics20. A typical entangled photon pair is obtained by a spontaneous parametric down-conversion (SPDC) process of the second-order nonlinear optics21. Because the wave mixing process of SPDC is coherent, a phase matching among the pump and two sibling photons is an inherent birth condition20,21,22,23. In that sense, an assumption of a specific phase relation between the entangled photons is not absurd. Recently, such an understanding has been presented for the Hong-Ou-Mandel (HOM) effect24,25 and Franson-type nonlocal correlation26 using the wave nature. Experimental demonstrations have also been conducted in trapped ions for a ππ/2 phase difference27. A complete analytical solution of the phase relation between entangled photons shows the same ππ/2 for the HOM effect25. For the nonlocal correlation between entangled photons, a coincidence measurement process for a particular product-basis selection is an essential condition5,22,26,28. Thus, the quantum feature should be understood differently.
Here, completely different methods of super-resolution29,30,31,32,33,34,35,36,37,38,39 and nonlocal correlation40,41,42 are presented using phase and frequency-controlled coherent photons, respectively, where the super-resolution is to overcome the standard quantum limit (SQL) toward the Heisenberg limit, as shown by photonic de Broglie wave (PBWs)29,30,31,32, N00N states35,36,37,38,39, or squeezed state39. Classically excited super-resolution has also been observed for the Heisenberg limit in quantum sensing using phase-controlled coherent photons33,34 via the projection method37 in a non-interferometric system. For the coherence manipulations of the phase control for super-resolution, a quarter-wave plate (QWP) is inserted before the polarizer in the quantum eraser scheme of Fig. 119. The QWP-caused phase shift between orthogonal polarization bases of coherent photon results in fringe shifts between with and without QWP-based quantum erasers (see Fig. 2)43. For the coherently excited nonlocal correlations, a pair of acousto-optic modulators (AOMs) are used to induce the polarization-frequency correlation for post-determined coincidence measurements25. For the excitation of the coherently excited nonlocal quantum features between quantum erasers, a selective measurement technique plays a key role for the inseparable intensity products, where DC components are blocked.
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