Single-photon Bell state measurement based on a quantum random walk

Bell state measurement (BSM) plays an important role in quantum information processing. However, a complete BSM cannot be achieved with linear optics with current technology. In this paper, we present a scheme for realizing single-photon BSM via a one-dimensional photonic quantum random walk. In our scheme, the maximally entangled states with polarization and path degrees of freedom are used as Bell states; then a complete BSM based on quantum random walk can be implemented in single-photon Hilbert space. Detecting single-photon count at different positions can provide unambiguous discrimination of all four Bell states to verify our scheme. Furthermore, we also discuss how to apply our BSM scheme to the proposed single-photon cryptography system.