In this work, we give an analytical derivation of the reduced density matrix between two qubits in a cavity field, which is described by the quantum Rabi model. Using the coherent state method and the generalized hypergeometric functions, we find a complete solution of the 4-by-4 reduced density matrix for each eigen energy by taking the partial trace over the cavity field states. Four kinds of measurements used to describe the quantum entanglement and quantum correlation between the two qubits, i.e., the concurrence, quantum discord, steerable weight, and robustness of coherence, are calculated for the ground state and excited states. For both the weak coupling (\(g\rightarrow 0\)) and deep-strong coupling (\(g\rightarrow \infty \)) regimes, quantum entanglement and quantum correlation between the two qubits are vanishing. An appropriate coupling in the deep strong coupling regime between the qubits and the cavity field is required if one wants to establish quantum entanglement between the qubits.

在这项工作中，我们给出了腔场中两个量子位之间的密度降低矩阵的解析推导，这由量子Rabi模型描述。使用相干态方法和广义超几何函数，我们通过对腔场状态进行部分跟踪，找到了每个本征能量的4×4缩减密度矩阵的完整解。针对基态和激发态，计算了用于描述两个量子位之间的量子纠缠和量子相关性的四种量度，即并发性，量子不和谐性，可控制权重和相干性。对于弱耦合（\（g \ rightarrow 0 \））和深强耦合（\（g \ rightarrow \ infty \））体制，两个量子位之间的量子纠缠和量子相关性正在消失。如果要在量子位之间建立量子纠缠，则需要在量子位和腔场之间的深强耦合机制中进行适当的耦合。