The evolution of quantum coherence in a qubit is analyzed, over short and long times, in case the qubit interacts with a bosonic environment. The distribution of the frequency modes exhibits a low-frequency band gap. The initial conditions under study of the qubit and the bosonic environment are factorized or prepared with selective or nonselective measurements. The modulus of the coherence term of the reduced density matrix of the qubit evolves algebraically over short times and, due to the band gap, tends to the nonvanishing asymptotic value with damped oscillations. Depending on the measurement scheme, the nonselective preparation measurement can enhance quantum coherence or accelerate the decoherence process, over short times, according to dominant linear laws. Over long times, the nonselective preparation measurement produces the slowest-decaying envelope of the damped oscillations among the decoherence processes under study. Similar short- and long-time evolution is exhibited by the trace distance measure of two general states of the qubit.

中文翻译：

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由带隙和初始状态制备测量引起的量子相干性的演变

在短时间和长时间内分析量子位中量子相干性的演变，以防量子位与玻色子环境相互作用。频率模式的分布呈现出低频带隙。量子比特和玻色子环境研究的初始条件通过选择性或非选择性测量进行分解或准备。量子位的降低密度矩阵的相干项的模数在短时间内以代数方式演变，并且由于带隙，趋向于具有阻尼振荡的非零渐近值。根据主要的线性定律，根据测量方案，非选择性制备测量可以在短时间内增强量子相干性或加速退相干过程。长期以来，非选择性制备测量在所研究的退相干过程中产生衰减振荡的最慢衰减包络。量子比特的两种一般状态的迹线距离测量显示出类似的短期和长期演化。