Coherence depletion in the Grover quantum search algorithm
Coherence depletion in the Grover quantum search algorithm
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Grover 量子搜索算法中的相干性损耗
DOI：
10.1103/physreva.95.032307
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发表时间：
2017-03-07
影响因子：
2.9
通讯作者：
Fan, Heng
中科院分区：
文献类型：
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作者：
Shi, Hai-Long;Liu, Si-Yuan;Fan, Heng
通过几种典型的量子相干性和量子关联性测度，研究了量子相干性损耗（QCD）在Grover搜索算法（GA）中的作用。利用相干测度的相对熵，我们证明了量子色动力学的成功概率依赖于量子色动力学。同样的现象也被发现，通过使用的l1范数的相干性措施（Cl 1）。在极限情况下，定义了QCD在提高GA成功概率方面的性能指标，该性能指标只与数据库的规模和样本个数有关，而与使用Cr或Cl 1无关.在广义Grover搜索算法（GGA）中，一类状态的QCD随所需的最佳测量时间而增加。相比之下，在GA中的其他量子关联的量化，如成对纠缠，多体纠缠，成对不和谐，真正的多体不和谐，不能直接相关的成功概率或最佳测量时间。此外，我们没有检测成对非局部性或真正的三方非局部性在GA中，因为Clauser-Horne-Shimony-Holt不等式和Svetlichny不等式没有被违反。
We investigate the role of quantum coherence depletion ( QCD) in the Grover search algorithm ( GA) by using several typical measures of quantum coherence and quantum correlations. By using the relative entropy of coherence measure ( Cr), we show that the success probability depends on the QCD. The same phenomenon is also found by using the l1 norm of coherence measure ( Cl1). In the limit case, the cost performance is defined to characterize the behavior about QCD in enhancing the success probability of GA, which is only related to the number of searcher items and the scale of the database, regardless of using Cr or Cl1. In the generalized Grover search algorithm ( GGA), the QCD for a class of states increases with the required optimal measurement time. In comparison, the quantification of other quantum correlations in GA, such as pairwise entanglement, multipartite entanglement, pairwise discord, and genuine multipartite discord, cannot be directly related to the success probability or the optimal measurement time. Additionally, we do not detect pairwise nonlocality or genuine tripartite nonlocality in GA since Clauser-Horne-Shimony-Holt inequality and Svetlichny's inequality are not violated.