Zhang Zhou, Dai Yue, Dong Yu-Li, Zhang Chengjie
School of Physical Science and Technology, Soochow University, Suzhou, 215006, China.
School of Physical Science and Technology, Ningbo University, Ningbo, 315211, China.
Sci Rep. 2020 Jul 21;10(1):12122. doi: 10.1038/s41598-020-68979-z.
Quantifying coherence and entanglement is extremely important in quantum information processing. Here, we present numerical and analytical results for the geometric measure of coherence, and also present numerical results for the geometric measure of entanglement. On the one hand, we first provide a semidefinite algorithm to numerically calculate geometric measure of coherence for arbitrary finite-dimensional mixed states. Based on this semidefinite algorithm, we test randomly generated single-qubit states, single-qutrit states, and a special kind of d-dimensional mixed states. Moreover, we also obtain an analytical solution of geometric measure of coherence for a special kind of mixed states. On the other hand, another algorithm is proposed to calculate the geometric measure of entanglement for arbitrary two-qubit and qubit-qutrit states, and some special kinds of higher dimensional mixed states. For other states, the algorithm can get a lower bound of the geometric measure of entanglement. Randomly generated two-qubit states, the isotropic states and the Werner states are tested. Furthermore, we compare our numerical results with some analytical results, which coincide with each other.
在量子信息处理中，量化相干性和纠缠极为重要。在此，我们给出了相干性几何度量的数值和解析结果，同时也给出了纠缠几何度量的数值结果。一方面，我们首先提供一种半定算法，用于数值计算任意有限维混合态的相干性几何度量。基于此半定算法，我们测试了随机生成的单量子比特态、单量子三态以及一种特殊的d维混合态。此外，我们还得到了一种特殊混合态相干性几何度量的解析解。另一方面，提出了另一种算法来计算任意两量子比特和量子比特 - 量子三态以及某些特殊的高维混合态的纠缠几何度量。对于其他态，该算法可以得到纠缠几何度量的一个下界。测试了随机生成的两量子比特态、各向同性态和维纳态。此外，我们将数值结果与一些解析结果进行了比较，它们相互吻合。
