一句话：证明量子优势的出现由刻画 CSP 多态恒等式与复杂度的 minion 决定，并给出图与一般关系结构上的刻画。
本文研究以关系结构间同态建模的信息处理任务：当纠缠被用作计算资源时，这类任务何时表现出量子优势。作者证明，量子优势的出现由一种与刻画 CSP 多态恒等式、进而与 CSP 复杂度相同的代数结构（minion）决定。文章进一步考察量子优势 minion 与已知控制 CSP 可处理性（tractability）和宽度（width）的 minion 之间的联系，并借助 CSP 代数理论中的复杂度结果，对图情形下的量子优势给出刻画，同时对任意关系结构给出新的必要与充分条件。
Information-processing tasks modelled by homomorphisms between relational structures can witness quantum advantage when entanglement is used as a computational resource. We prove that the occurrence of quantum advantage is determined by the same type of algebraic structure (known as a minion) that captures the polymorphism identities of CSPs and, thus, CSP complexity. We investigate the connection between the minion of quantum advantage and other known minions controlling CSP tractability and width. In this way, we make use of complexity results from the algebraic theory of CSPs to characterise the occurrence of quantum advantage in the case of graphs, and to obtain new necessary and sufficient conditions in the case of arbitrary relational structures.