This chapter introduces the concept of coherence and discuss the coherent property of radiation. The author starts from Einstein’s granularity picture of light to introduce two category of superpositions in terms of Einstein’s subfields and Maxwell’s Fourier-modes. Einstein’s picture of light is still in the framework of electromagnetic theory of radiation, except the concept of “bundle of ray” added additional freedom to the superposition of Fourier mode. The physics the authors consider now is the coherent or incoherent superposition among these subfields that are created from these spatially separated sub-sources. If these subfields are able to superpose coherently people consider the radiation spatially coherent; otherwise, the radiation is spatially incoherent. It is interesting to see the similarities between temporal wavepacket in the longitudinal dimension and the spatial wavepacket in the transverse dimension. The temporal coherence of the radiation produces temporal wavepackets, implying temporal constructive-destructive interference; and the spatial coherence of the radiation results in spatial wavepackets, implying spatial constructive-destructive interference.
The time evolution of one- and two-dimensional discrete-time quantum walk with increase in disorder is studied. We use spatial, temporal and spatio-temporal broken periodicity of the unitary evolution as disorder to mimic the effect of disordered/random medium in our study. Disorder induces a dramatic change in the interference pattern leading to localization of the quantum walks in one- and two-dimensions. Spatial disorder results in the decreases of the particle and position entanglement in one-dimension and counter intuitively, an enhancement in entanglement with temporal and spatio-temporal disorder is seen. The study signifies that the Anderson localization of quantum state without compromising on the degree of entanglement could be implement in a large variety of physical settings where quantum walks has been realized. The study presented here could make it feasible to explore, theoretically and experimentally the interplay between disorder and entanglement. This also brings up a variety of intriguing questions relating to the negative and positive implications on algorithmic and other applications.