表示多量子比特么正演化的自旋相干性和无穷小相干性
Representing multiqubit unitary evolutions: spin coherences and infinitesimal coherences
摘要：
对于多量子比特密度算符的相干参数化张量，我们给出了相应的微元幺正动力学的显式表达式。这种形式主义的主要优点（清楚地让人想起自旋系统的“相干性”和“耦合哈密顿”的概念）是量子位之间的相关模式和无穷小相关模式同时突出显示，并且可以建设性地用于量子位操作。例如，它允许显式计算非局部哈密顿量的单参数轨道的罗德里格斯公式。这个结果很容易推广到Cartan子代数的轨道上，并且可以把酉传播子的Cartan分解写成线性作用。
英文摘要：
For the tensor of coherences parametrization of a multiqubit density operator, we provide an explicit formulation of the corresponding unitary dynamics at infinitesimal level. The main advantage of this formalism (clearly reminiscent of the idea of ``coherences'' and ``coupling Hamiltonians'' of spin systems) is that the pattern of correlation between qubits and the pattern of infinitesimal correlation are highlighted simultaneously and can be used constructively for qubit manipulation. For example, it allows to compute explicitly a Rodrigues' formula for the one-parameter orbits of nonlocal Hamiltonians. The result is easily generalizable to orbits of Cartan subalgebras and allows to write the Cartan decomposition of unitary propagators as a linear action.
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