Some geometric interpretations of quantum fidelity
Some geometric interpretations of quantum fidelity
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DOI：
10.1016/j.laa.2015.08.037
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发表时间：
2015-03
影响因子：
1.1
通讯作者：
Jin Li;Rajesh Pereira;S. Plosker
中科院分区：
文献类型：
--
作者：
Jin Li;Rajesh Pereira;S. Plosker
我们考虑两个态ρ和σ之间的量子保真度，其中我们固定ρ并允许σ通过量子信道发送。我们确定最小保真度，其中一个最小化（a）所有酉通道，（B）所有混合酉通道，和（c）任意通道。我们得到的结果涉及ρ的最小特征值，我们可以解释为一个凸组合系数。因此，我们给出了一个新的几何解释的最小保真度相对于封闭的，凸集的密度矩阵和相对于封闭的，凸集的量子通道。我们进一步研究保真度的几何性质，通过考虑密度矩阵作为子空间上的归一化投影而产生;这样，保真度可以被视为两个空间之间距离的几何度量。我们给出了保真度和子空间之间的正则（主）角之间的连接。
We consider quantum fidelity between two statesρandσ, where we fixρand allowσto be sent through a quantum channel. We determine the minimal fidelity where one minimizes over (a) all unital channels, (b) all mixed unitary channels, and (c) arbitrary channels. We derive results involving the minimal eigenvalue ofρ, which we can interpret as a convex combination coefficient. As a consequence, we give a new geometric interpretation of the minimal fidelity with respect to the closed, convex set of density matrices and with respect to the closed, convex set of quantum channels. We further investigate the geometric nature of fidelity by considering density matrices arising as normalized projections onto subspaces; in this way, fidelity can be viewed as a geometric measure of distance between two spaces. We give a connection between fidelity and the canonical (principal) angles between the subspaces.