Direct and efficient detection of quantum superposition

One of the most striking quantum phenomena is superposition, where one particle simultaneously inhabits different states. Most methods to verify coherent superposition are indirect, in that they require the distinct states to be recombined. Here, we adapt an xor game, in which a “test” photon is placed in a superposition of two orthogonal spatial modes, and each mode is sent to separated parties who perform local measurements on their modes without reinterfering the original modes. We show that by using a second identical “measurement” photon the parties are nonetheless able to verify if the test photon was placed in coherent superposition of the two spatial modes. We then turn this game into a resource-efficient verification scheme, obtaining a confidence that the particle is superposed which approaches unity exponentially fast. We demonstrate our scheme using a single photon, obtaining a 99% confidence that the particle is superposed with only 37 copies. Our work shows the utility of xor games to verify quantum resources, allowing us to efficiently detect quantum superposition without reinterfering the superposed modes.