Quantum-assisted rendezvous on hypercubes: a quantum Bernoulli noise approach

Abstract:We study quantum-assisted balanced rendezvous on the $d$-dimensional hypercube in a one-step two-agent quantum-walk framework, where the two agents move the same Hamming distance and meet at a common midpoint. The key structure is a projective $t$-sphere resolution, which governs exact finite-dimensional quantum attainment. Its scalar analogue recovers the corresponding classical characterization. We characterize finite-dimensional quantum attainment of the no-signalling benchmark, construct quantum strategies from projective sphere resolutions, and establish a rigidity theorem for optimal finite-dimensional strategies. A marked difference appears between nearest-neighbor and higher-cardinality updates: quantum advantage can occur in the former, whereas in the latter the geometry of the relevant Hamming spheres rules out exact finite-dimensional attainment of the no-signalling value. Together, these results connect quantum-walk dynamics, Hamming-sphere geometry, and quantum rendezvous within the quantum Bernoulli noises (QBN) framework.

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Combinatorics (math.CO); Probability (math.PR)

arXiv:2610.12949 [quant-ph]

(or arXiv:2610.12949v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.12949 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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