Experimental demonstration of quantum walks with initial superposition states

The preparation of initial superposition states of discrete-time quantum walks (DTQWs) are necessary for the study and applications of DTQWs. In linear optics, it is easy to prepare initial superposition states of the coin, which are always encoded by polarization states; while the preparation of superposition states of the walker is challenging. Based on a novel encoding method, we here propose a DTQW protocol in linear optics which enables the preparation of arbitrary initial superposition states of the walker and the coin. With this protocol, we report an experimental demonstration of DTQW with the walker initially in superposition states, by using only passive linear-optical elements. The effects of the walker's different initial superposition states on the spread speed of the DTQW and on the entanglement between the coin and the walker are also experimentally investigated, which have not been reported before. When the walker starts with superposition states, we show that the properties of DTQW are very different from those of DTQW starting with a single position. Our findings reveal different properties of DTQW and paves an avenue to study DTQW with arbitrary initial states. Moreover, the encoding method enables one to encode an arbitrary high-dimensional quantum state using a single physical qubit and may be adopted to implement other quantum information tasks.