AI 中文总结
从资源几何角度探索量子电池相干厄米熵提取，定义几何功率容量$\Pi_c(\rho)$，证明其为单位驱动范数下的容量，通过结合相关界得出一般界，制定相关容量，量子比特和三态例子表明其捕捉了相干放电的资源几何特征。
AI 中文摘要
我们从资源几何的角度探索量子电池中的相干厄米熵提取。对于初始态$\rho$，我们通过相干厄米熵$\mathcal{E}_c(\rho)$以及激活态$\sigma_\rho$与被动态$P_\rho$之间的相干提取距离$D_c^{\rm ext}(\rho)$来量化相干提取过程。这定义了几何功率容量$\Pi_c(\rho)=\mathcal{E}_c(\rho)/D_c^{\rm ext}(\rho)$，它衡量单位最小酉距离释放的相干厄米熵。我们证明，对于任何满足$\|V_t\|\leq\nu$的驱动哈密顿量，实际相干放电功率受限于$P_c^{\rm ext}(\rho;V_t)\leq \nu\Pi_c(\rho)$，表明$\Pi_c(\rho)$是单位驱动范数下的容量而非特定协议的功率。通过结合相干厄米熵的相对熵界与相干提取距离的几何界，得出了$\Pi_c(\rho)$的一般界。我们还制定了涉及给定哈密顿量有效速度的相干度量诱导界和协议校正容量。量子比特和量子三态的例子表明，$\Pi_c(\rho)$捕捉了相干放电的资源几何特征，超越了单独的相干厄米熵或相干度量。
英文摘要
We explore coherent ergotropy extraction in quantum batteries from a resource-geometric point of view. For an initial state $ρ$, we quantify the coherent extraction process by the coherent ergotropy $\mathcal{E}_c(ρ)$ and the coherent extraction distance $D_c^{\rm ext}(ρ)$ between the active state $σ_ρ$ and the passive state $P_ρ$. This defines the geometric power capacity $Π_c(ρ)=\mathcal{E}_c(ρ)/D_c^{\rm ext}(ρ)$, which measures the coherent ergotropy released unit minimal unitary distance. We prove that, for any driving Hamiltonian satisfying $\|V_t\|\leqν$, the actual coherent discharging power is bounded by $P_c^{\rm ext}(ρ;V_t)\leq νΠ_c(ρ)$, showing that $Π_c(ρ)$ is a capacity under unit driving norm rather than the power of a particular protocol. General bounds on $Π_c(ρ)$ are derived by combining relative entropy bounds on coherent ergotropy with geometric bounds on the coherent extraction distance. We also formulate coherence measure induced bounds and protocol-corrected capacities involving the effective speed of a given Hamiltonian. Qubit and qutrit examples demonstrate that $Π_c(ρ)$ captures a resource-geometric feature of coherent discharging beyond coherent ergotropy or coherence measures alone.
