The presence of quantum correlations in a quantum state is related to the state response to local unitary perturbations. Such response is quantified by the distance between the unperturbed and perturbed states, minimized with respect to suitably identified sets of local unitary operations. In order to be a bona fide measure of quantum correlations, the distance function must be chosen among those that are contractive under completely positive and trace preserving maps. The most relevant instances of such physically well behaved metrics include the trace, the Bures, and the Hellinger distance. To each of these metrics one can associate the corresponding discord of response, namely the trace, or Hellinger, or Bures minimum distance from the set of unitarily perturbed states. All these three discords of response satisfy the basic axioms for a proper measure of quantum correlations. In the present work we focus in particular on the Bures distance, which enjoys the unique property of being both Riemannian and contractive under completely positive and trace preserving maps, and admits important operational interpretations in terms of state distinguishability. We compute analytically the Bures discord of response for two-qubit states with maximally mixed marginals and we compare it with the corresponding Bures geometric discord, namely the geometric measure of quantum correlations defined as the Bures distance from the set of classically correlated quantum states. Finally, we investigate and identify the maximally quantum correlated two-qubit states according to the Bures discord of response. These states exhibit a remarkable nonlinear dependence on the global state purity.
Geometric quantum discord with Bures distance: the qubit case
二分系统AB的量子态到子系统A的经典态集的最小布勒斯距离定义了量子不协调的几何度量。当A是量子比特时，我们证明了这种几何量子不协调是由a（2 n B）x（2 n B）厄米矩阵的特征值给出的，n B是另一个子系统B的Hilbert空间维数.作为第一个应用程序，我们计算的DQC 1算法的输出状态的几何不和谐。我们发现，它需要它的最高值时，酉矩阵的算法计算的轨迹有其特征值均匀分布在单位圆模对称的原点。作为第二个应用，我们推导出一个显式公式的几何不和谐的两个量子比特状态的最大混合边缘，并比较它与其他措施的量子相关性。我们还确定了最接近这样的两个量子比特状态的经典状态。
Characterizing entanglement using quantum discord over state extensions
我们提出了一个框架来描述纠缠与量子不和谐，非对称和对称，状态扩展。特别地，我们证明了状态扩展上不和谐的最小Bures距离等价于纠缠的Bures距离。这种等价性将量子不和谐置于比纠缠概念上更原始的位置，因为纠缠可以被解释为所有状态扩展上的不和谐的不可约部分。在此基础上，我们还将纠缠的布勒斯距离与量子态判别联系起来，给出了它的运算意义。此外，对于相对熵部分，我们证明了Devi和Rajagopal [A. R.联合Devi和A. K. Rajagopal，Phys. Rev. Lett. 100，140502（2008）]实际上相当于纠缠的相对熵。我们还提供了几个量化的纠缠不和谐措施的基础上。
Geometric Response in Open Quantum Systems: Coherence, Curvature, and Susceptibility
University of Houston（休斯顿大学）；Université de Montréal（蒙特利尔大学）；Georgia Institute of Technology（佐治亚理工学院）；Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV)（国立理工大学高级研究中心）
