Undamped trace distance and coherence preservation of quantum bit in photonic crystal

We study the coherence preservation of quantum bit in photonic crystal using input-output trace distance. The input-output trace distance can be extremely short and the information hardly dissipates when the quantum bit frequency lies deep inside the photonic band gap. Different from the behavior in cavities, the undissipated information of the quantum bit can be held in the photonic band gap due to the effective interaction between the quantum bit and photonic crystal. A factor called coherence radius is defined in this paper for evaluating the quantum coherence preservation in photonic crystal, which is straightly linked to the visibility of input-output trace distance and the coherence of quantum states.