自旋量子比特与超导磁通量子比特热态流形上的 Bures 与 Sjoqvist 度量
Bures and Sjoqvist Metrics over Thermal State Manifolds for Spin Qubits and Superconducting Flux Qubits
AI总结：
本文分析了自旋与超导磁通量子比特热态流形上的 Bures 与 Sjoqvist 度量，发现两者在零温度极限外因相邻混合态不可交换性而产生差异，并探讨了其可观测后果。
摘要：
近年来，微分几何、统计物理学与量子信息科学之间的相互作用日益引起理论界的关注。本文针对特定的自旋量子比特和超导磁通量子比特 Hamiltonian 模型，显式分析了其热态流形上的 Bures 度量与 Sjoqvist 度量。尽管对于这两种 Hamiltonian 模型，在逆温度趋于无穷大的渐近极限情况下，这两种度量均同样简化为 Fubini-Study 度量，但我们观察到，当偏离零温度极限时，这两种度量通常是不同的。特别地，我们讨论了超导磁通 Hamiltonian 模型情形下的这种差异。我们得出结论，在相邻混合量子态不可交换性所指定的非经典行为存在时，这两种度量存在差异。反过来，这种不可交换性也由这两种度量以不同方式进行了量化。最后，我们简要讨论了当使用这两种度量预测量子信息科学中感兴趣的物理系统的临界和/或复杂行为时，它们之间这种差异的可能可观测后果。
英文摘要：
The interplay among differential geometry, statistical physics, and quantum information science has been increasingly gaining theoretical interest in recent years. In this paper, we present an explicit analysis of the Bures and Sjoqvist metrics over the manifolds of thermal states for specific spin qubit and the superconducting flux qubit Hamiltonian models. While the two metrics equally reduce to the Fubini-Study metric in the asymptotic limiting case of the inverse temperature approaching infinity for both Hamiltonian models, we observe that the two metrics are generally different when departing from the zero-temperature limit. In particular, we discuss this discrepancy in the case of the superconducting flux Hamiltonian model. We conclude the two metrics differ in the presence of a nonclassical behavior specified by the noncommutativity of neighboring mixed quantum states. Such a noncommutativity, in turn, is quantified by the two metrics in different manners. Finally, we briefly discuss possible observable consequences of this discrepancy between the two metrics when using them to predict critical and/or complex behavior of physical systems of interest in quantum information science.
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