We present an information geometric analysis of both entropic speeds and entropy production rates arising from geodesic evolution on manifolds parametrized by pure quantum states. In particular, we employ pure states that emerge as outputs of suitably chosen su(2; ℂ) time-dependent Hamiltonian operators that characterize analog quantum search algorithms of specific types. The su(2; ℂ) Hamiltonian models under consideration are specified by external time-dependent magnetic fields within which spin-1/2 test particles are immersed. The positive definite Riemannian metrization of the parameter manifold is furnished by the Fisher information function. The Fisher information function is evaluated along parametrized squared probability amplitudes obtained from the temporal evolution of these spin-1/2 test particles. A minimum action approach is then utilized to induce the transfer of the quantum system from its initial state to its final state on the parameter manifold over a finite temporal interval. We demonstrate in an explicit manner that the minimal (that is, optimum) path corresponds to the shortest (that is, geodesic) path between the initial and final states. Furthermore, we show that the minimal path serves also to minimize the total entropy production occurring during the transfer of states. Finally, upon evaluating the entropic speed as well as the total entropy production along optimal transfer paths within several scenarios of physical interest in analog quantum searching algorithms, we demonstrate in a transparent quantitative manner a correspondence between a faster transfer and a higher rate of entropy production. We therefore conclude that higher entropic speed is associated with lower entropic efficiency within the context of quantum state transfer.

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量子态演化具有最小熵产生的概率路径的信息几何方面

我们对由纯量子态参数化的流形上的测地线演化产生的熵速度和熵产生率进行了信息几何分析。In particular, we employ pure states that emerge as outputs of suitably chosen苏(2; ℂ)表征特定类型的模拟量子搜索算法的时间相关哈密顿算子。这苏(2; ℂ)正在考虑的哈密顿模型由外部时间相关磁场指定，其中自旋-1/2浸没试验颗粒。参数流形的正定黎曼度量由 Fisher 信息函数提供。Fisher 信息函数是根据从这些自旋的时间演化中获得的参数化平方概率幅度进行评估的。1/2测试粒子。然后使用最小作用方法来诱导量子系统在有限时间间隔内从其初始状态转移到参数流形上的最终状态。我们以明确的方式证明了最小（即最佳）路径对应于初始状态和最终状态之间的最短（即测地线）路径。此外，我们表明，最小路径还有助于最小化状态转移期间发生的总熵产生。最后，在模拟量子搜索算法的几个物理感兴趣的场景中评估熵速度以及沿最佳传输路径的总熵产生后，我们以透明的定量方式证明了更快的传输和更高的熵产生率之间的对应关系.