We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including measurement. We provide universal categorical constructions that semantically interpret this arrow metalanguage with choice, starting with any rig groupoid interpreting the reversible base language. Several properties of quantum measurement follow in general, and we translate quantum flow charts into our language. The semantic constructions turn the category of unitaries between Hilbert spaces into the category of completely positive trace-preserving maps, and they turn the category of bijections between finite sets into the category of functions with chosen garbage. Thus they capture the fundamental theorems of classical and quantum reversible computing of Toffoli and Stinespring.

翻译：我们研究两种双重量子信息效应,以在量计算中操纵信息量:隐藏和分配。由此产生的类型和影响系统充分表达不可逆转量计算,包括测量。我们提供通用的绝对构造,从任何可逆基语言的钻机组开始,以选择的方式对箭头元语言进行精度解释。量量测量的几种特性一般都遵循,我们将量子流图翻译成我们的语言。语义构造将希尔伯特空间之间的单位类别转换成完全肯定的痕量保存地图类别,并将定数组之间的两分类别转换成选择垃圾的功能类别。因此它们捕捉了托夫利和斯坦斯普林的经典和量子可逆计算的基本原理。