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

@misc{wang2026quantumassisted,
  title = {{Quantum-assisted rendezvous on hypercubes: a quantum Bernoulli noise approach}},
  author = {Ce Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12949},
  eprint = {2610.12949},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12949},
}

TY  - UNPB
TI  - Quantum-assisted rendezvous on hypercubes: a quantum Bernoulli noise approach
AU  - Ce Wang
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.12949
UR  - https://arxiv.org/abs/2610.12949
AB  - 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.
ER  -