We investigated discrete-time quantum walks with an arbitary unitary coin.Here we discover that the average position x=max（x） sin（α＋γ）,while the initial state is 1/2～（1/2）（｜0L＋i｜0R）.We verify the result,and obtain some symmetry properties of quantum walks with a U（2） coin with ｜0L and ｜0R as the initial state.
Quantum beats can be produced in fourth-order interference such as in a Hong–Ou–Mandel(HOM) interferometer by using photons with different frequencies.Here we present theoretically the appearance of interference of quantum beats when the HOM interferometer is combined with a Franson-type interferometer.This combination can make the interference effect of photons with different colors take place not only within the coherence time of downconverted fields but also in the region beyond that.We expect that it can provide a new method in quantum metrology,as it can realize the measurement of time intervals in three scales.
