论文标题
混合量子合奏的平行性
Parallelity of mixed quantum ensembles
论文作者
论文摘要
引入了一个统一的框架，用于识别密度运算符分解的距离和载体。量子集合之间的并行性是通过最大程度地减少允许分解的距离来定义的。最小值是一对状态的特性，与Bures距离重合。并行条件施加了一种连接（平行传输规则），该连接导致密度运算符序列的Uhlmann载体。密度运算符的光谱分解的距离和载体被确定为对完整分解自由的亚组限制。这些光谱概念是混合量子集合的规范不变（分解独立）性能，只要相应的密度算子是非分化的。获得混合量子状态离散序列的仪表不变的光谱几何相是获得光谱载体痕迹的相位的。该几何相在连续极限下与干涉混合状态几何相的不同。
A unifying framework for identifying distance and holonomy for decompositions of density operators is introduced. Parallelity between quantum ensembles is defined by minimizing this distance over allowed decompositions. The minimum is a property of a pair of states and coincides with the Bures distance. The parallelity condition imposes a connection (rule for parallel transport) that results in the Uhlmann holonomy for sequences of density operators. A distance and holonomy for spectral decompositions of density operators is identified as a sub-group restriction of the full decomposition freedom. These spectral concepts are gauge invariant (decomposition independent) properties of mixed quantum ensembles, as long as the corresponding density operators are non-degenerate. A gauge invariant spectral geometric phase for discrete sequences of mixed quantum states is obtained as the phase of the trace of the spectral holonomy. This geometric phase differs from the interferometric mixed state geometric phase in the continuous limit.
