Perfect State Transfer in Arbitrary Distance

• URL: http://arxiv.org/abs/2212.11699v1
• Date: Thu, 22 Dec 2022 13:45:28 GMT
• Title: Perfect State Transfer in Arbitrary Distance
• Authors: Supriyo Dutta
• Abstract summary: Quantum Perfect State Transfer (PST) is a fundamental tool of quantum communication in a network. We introduce a significantly powerful method for PST based on the Markovian quantum walk.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $0 \leq j < \frac{n - 1}{2}$. 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 $j = 0, 1, \dots (m - 1)$ in a cycle graph with $2m$ vertices.

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