Pretty good quantum fractional revival in paths and cycles
Pretty good quantum fractional revival in paths and cycles
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DOI：
10.5802/alco.189
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发表时间：
2022-01
影响因子：
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通讯作者：
Ada Chan;Whitney A. Drazen;Or Eisenberg;Mark Kempton;Gábor Lippner
中科院分区：
文献类型：
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作者：
Ada Chan;Whitney A. Drazen;Or Eisenberg;Mark Kempton;Gábor Lippner
我们开始了对图中相当好的量子分数恢复的研究，它是图中相当好的量子态转移的推广。利用图的邻接矩阵的特征值和特征向量，给出了图中相当好的分式再生的完全刻画。这个刻画源于Kronecker关于丢番图近似的一个引理，并且类似于图中相当好的状态转移的谱刻画。利用这一点，我们给出了路径和循环中何时可以出现相当好的分数恢复的完整刻画。
We initiate the study of pretty good quantum fractional revival in graphs, a generalization of pretty good quantum state transfer in graphs. We give a complete characterization of pretty good fractional revival in a graph in terms of the eigenvalues and eigenvectors of the adjacency matrix of a graph. This characterization follows from a lemma due to Kronecker on Diophantine approximation, and is similar to the spectral characterization of pretty good state transfer in graphs. Using this, we give complete characterizations of when pretty good fractional revival can occur in paths and in cycles.