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.

翻译：以关系结构间的同态建模的信息处理任务中，当纠缠被用作计算资源时，可以展现量子优势。我们证明，量子优势的产生由与约束满足问题（CSP）的多态恒等式相同的代数结构（称为"小集团"）决定，从而也与CSP复杂性密切相关。我们研究了控制CSP可解性与宽度的其他已知小集团与量子优势小集团之间的联系。通过这种方法，我们利用CSP代数理论中的复杂性结果，刻画了图情形下量子优势的产生条件，并为任意关系结构情形下的充要条件提供了新的判定依据。