Spectral Criterion for Disorder-Free Localization of Quantum Walks on Hypercube: QBN Approach

Abstract:We study disorder-free localization in a spin-coupled quantum walk on the hypercube within the quantum Bernoulli noises framework. We derive a general criterion for disorder-free localization: it occurs if and only if some spectral subspace of a reduced unitary evolution contains a vector whose position marginal probability is non-uniform. For the Grover walk with distance-dependent coupling \(\phi_\sigma=|\sigma|\pi/(n+1)\) in dimension \(d=4\), we explicitly construct a non-uniform fixed point in the all \(+1\) spin configuration. This implies that disorder-free localization occurs in our model.

17 pages, 2 tables. Any comments are welcome

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Functional Analysis (math.FA); Probability (math.PR)

arXiv:2609.07267 [quant-ph]

(or arXiv:2609.07267v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.07267 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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