State transfer in chiral quantum walks

The chiral quantum walk is an emerging tool for state transfer as it helps circumvent the barrier of no-go theorems in quantum transport. Yet, it remains largely unexplored. We prove a conjecture that universal monogamy violations for perfect quantum transfer in large graphs require couplings beyond the simple imaginary [Formula: see text]. This motivates our constructions of new monogamy violations on sparse graph products. Then, we show a novel violation of periodicity and the first known examples of one-way perfect quantum transfer via transcendental couplings.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.