Starting from Polchinski’s thought experiment on how to distinguish between pure and thermal states, we construct a specific system to study the interaction between qubit and cavity quantum field theory (QFT) in order to provide a more operational point of view. Without imposing any restrictions on the initial states of qubit and cavity QFT, we compute the evolution of the system order by order by the perturbation method. We choose Landauer’s principle, an important bound in quantum computation and quantum measurement, as the basis for the determination of the thermal state. By backtracking the initial state form, we obtain the conditions that must be satisfied by the cavity QFT: the expectation value of the annihilation operator should be zero, and the expectation value of the particle number operator should satisfy the Bose–Einstein distribution. We also discuss the difference between the thermal state and a possible alternative to the thermal state: the canonical thermal pure quantum (CTPQ) state.

我们从Polchinski关于如何区分纯态和热态的思想实验出发，构建了一个具体的系统来研究量子比特和腔量子场论（QFT）之间的相互作用，以提供更具操作性的观点。在不对量子位和腔 QFT 的初始状态施加任何限制的情况下，我们通过微扰方法逐阶计算系统的演化。我们选择兰道尔原理（量子计算和量子测量的重要界限）作为确定热态的基础。通过回溯初始状态形式，我们得到了腔QFT必须满足的条件：湮没算子的期望值应为零，粒子数算子的期望值应满足玻色-爱因斯坦分布。我们还讨论了热态和热态的可能替代方案：规范热纯量子（CTPQ）态之间的差异。