Average position in quantum walks with a U(2) coin
Min Li, Yong-Sheng Zhang, Guang-Can Guo · Chinese Physics B · 2013
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(|0 L ⟩+i|0 R ⟩). We verify the result, and obtain some symmetry properties of quantum walks with a U(2) coin with |0 L 〉 and |0 R 〉 as the initial state.