一句话：提出两种 ZX-Calculus 完备公理化，规则近乎极小且具物理直观，并引入 ZX 图奇异值分解证明其充分性。
ZX-Calculus 此前虽已有完备公理化，但为达到完备性引入的公理数量多、操作繁琐且缺乏物理解释。本文针对一般 ZX-Calculus 提出两种完备公理化，认为其接近最优：所有等式均必要，且每条规则都有良好物理意义。作者引入 ZX 图的奇异值分解，并以此证明旧公理化中的所有规则都可由新公理化推出，从而建立新系统的完备性与充分性。该工作显著简化并解释了纯量子比特量子力学中的图形化推理。
Recent developments in the ZX-Calculus have resulted in complete axiomatisations first for an approximately universal restriction of the language, and then for the whole language. The main drawbacks were that the axioms that were added to achieve completeness were numerous, tedious to manipulate and lacking a physical interpretation. We present in this paper two complete axiomatisations for the general ZX-Calculus, that we believe are optimal, in that all their equations are necessary and moreover have a nice physical interpretation. To do so, we introduce the singular-value decomposition of a ZX-diagram, and use it to show that all the rules of the former axiomatisation are provable with the new one.