Abstract
We implemented a joint weak measurement of the trajectories of two photons in a photonic version of Hardy's experiment. The joint weak measurement has been performed via an entangled meter state in polarization degrees of freedom of the two photons. Unlike Hardy's original argument in which the contradiction is inferred by retrodiction, our experiment reveals its paradoxical nature as preposterous values actually read out from the meter. Such a direct observation of a paradox gives us new insights into the spooky action of quantum mechanics.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. In quantum mechanics, we often fall into difficulties when deciding the value of a physical quantity in the middle of a time evolution. Hardy's paradox, a photonic version of which is shown in the figure, is one of the most striking examples. We constructed this interferometer and observed the trajectories of photons via weak measurement, which causes little disturbance on the interferometer in a single run but still reveals information on the trajectories after many repetitions of the same experiment.
Main results. In our experiment, we implemented weak measurement by imprinting the path information onto polarizations of the photons with adjustable strength. We separately confirmed that the readouts of the measurement faithfully revealed path information, and that disturbances on the interferometers were small. Then we recorded the readouts when simultaneous detection occurred. The recorded results showed the paradoxical nature, namely, they indicated that for each photon, the probability of taking the overlapping arm was almost unity, while the joint probability was around zero.
Wider implications. Quantum paradoxes have often been discussed through logical inferences on physical quantities that are beyond the reach of experimental observation. Through weak measurement, we have revealed a paradoxical nature of quantum mechanics in a more direct way, namely, via experimental observation. We hope our results offer a renewed insight into the foundations of quantum mechanics.
Figure. Photonic version of Hardy's paradox. MZ1 is adjusted such that photon 1 arrives at C1 only if MZ1 has been disturbed by photon 2. The same goes for MZ2. When both detectors detect photons simultaneously, we may thus infer that photon 1 has taken the path O1, and that photon 2 has taken O2. However, if two photons encounter each other at BS3, a two-photon interference effect would force them to exit from the same side of BS3, and hence there should be no simultaneous detection.