论文标题
量子机械演变的最小熵生产路径的信息几何学方面
Information Geometry Aspects of Minimum Entropy Production Paths from Quantum Mechanical Evolutions
论文作者
论文摘要
我们介绍了在参数化量子状态的流形上，对熵速度和熵产生速度的信息几何分析。这些纯状态出现为合适的SU（2; c）时间依赖性的哈密顿运营商的输出，用于描述不同类型的模拟量子搜索方案。歧管上的Riemannian Metrrize是由通过分析SU（2; C）Hamiltonian模型的外部时间相关磁场中的Spin-1/2粒子在外部时间相关的磁场中对Spin-1/2粒子的时间量子机械演化而获得的，通过参数化平方概率幅度进行了评估的Fisher信息。我们采用一种最小动作方法将量子系统从初始状态转移到有限的时间间隔的歧管上的最终状态。此外，我们证明了最小化（最佳）路径是两种状态之间最短的（地球）路径，尤其是最小化在转移期间发生的总熵产生。最后，通过在模拟量子搜索问题的许多物理场景中评估熵速度和沿最佳转移路径的总熵产生，我们以明确的定量方式显示，在那里更快的传递对应于较高的熵生产率。因此，我们得出的结论是，较低的熵效率值似乎伴随着量子传输过程中较高的熵速度值。
We present an information geometric analysis of entropic speeds and entropy production rates in geodesic evolution on manifolds of parametrized quantum states. These pure states emerge as outputs of suitable su(2; C) time-dependent Hamiltonian operators used to describe distinct types of analog quantum search schemes. The Riemannian metrization on the manifold is specified by the Fisher information evaluated along the parametrized squared probability amplitudes obtained from analysis of the temporal quantum mechanical evolution of a spin-1/2 particle in an external time-dependent magnetic field that specifies the su(2; C) Hamiltonian model. We employ a minimum action method to transfer a quantum system from an initial state to a final state on the manifold in a finite temporal interval. Furthermore, we demonstrate that the minimizing (optimum) path is the shortest (geodesic) path between the two states, and, in particular, minimizes also the total entropy production that occurs during the transfer. Finally, by evaluating the entropic speed and the total entropy production along the optimum transfer paths in a number of physical scenarios of interest in analog quantum search problems, we show in a clear quantitative manner that to a faster transfer there corresponds necessarily a higher entropy production rate. Thus, we conclude that lower entropic efficiency values appear to accompany higher entropic speed values in quantum transfer processes.
