  The simplest single-photon entanglement is the entanglement of the vacuum
state and the single-photon state between two path modes. The verification of
the existence of single-photon entanglement has attracted extensive research
interests. Here, based on the construction of Bell's inequality in wave space,
we propose a new method to verify single photon entanglement. Meanwhile, we
define the wave state in two-dimensional space relative to the photon number
state, and propose a method to measure it. Strong violation of Bell inequality
based on joint measurement of wave states indicates the existence of single
photon entanglement with certainty. Wave state entanglement obtained from
Fourier transform of single photon entanglement and the corresponding
measurement protocols will provide us with more information-carrying schemes in
the field of quantum information. The difference in the representation in
photon-number space and wave space implies the wave-particle duality of single
photon entanglement.
