Subspace State Transfer in Coined Quantum Walks

• URL: http://arxiv.org/abs/2511.06750v1
• Date: Mon, 10 Nov 2025 06:29:29 GMT
• Title: Subspace State Transfer in Coined Quantum Walks
• Authors: Yichi Xu, Hanmeng Zhan,
• Abstract summary: We study a transport phenomenon in certain coined quantum walks where a subspace localized at a state gets transferred to another state.<n>We first develop characterizations for perfect and pretty good subspace state transfer using the spectral properties of a Hermitian digraph.<n>We then provide a weighted-time algorithm that tests whether perfect pointwise subspace state transfer occurs at an integer step.
• Score: 0.18650477793598305
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a transport phenomenon in certain coined quantum walks where a subspace of states localized at a vertex gets transferred to another vertex. We first develop characterizations for perfect and pretty good subspace state transfer using the spectral properties of a Hermitian weighted digraph obtained from the underlying graph. We then provide a polynomial-time algorithm that tests whether perfect pointwise subspace state transfer occurs at an integer step, given that the subspace and coins are rational. Finally, we construct several infinite families of examples that admit perfect pointwise $d$-dimensional subspace state transfer where $d\ge 2$.

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