Perfect State Transfer in Arbitrary Distance
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Quantum Perfect State Transfer (PST) is a fundamental tool of quantum communication in a network. It is considered a rare phenomenon. The original idea of PST depends on the fundamentals of the continuous-time quantum walk. A path graph with at most three vertices allows PST. Based on the Markovian quantum walk, we introduce a significantly powerful method for PST in this article. We establish PST between the extreme vertices of a path graph of arbitrary length. Moreover, any pair of vertices j and n - j - 1 in a path graph with n vertices allow PST for 0 ≤ j < n - 1/2. Also, no cycle graph with more than 4 vertices does not allow PST based on the continuous-time quantum walk. In contrast, we establish PSTs based on Markovian quantum walk between the pair of vertices j and j + m for j = 0, 1, … (m - 1) in a cycle graph with 2m vertices.
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