Classical and quantum structuralism
Classical and quantum structuralism
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古典和量子结构主义
DOI：
10.1017/cbo9781139193313.003
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Dusko Pavlovic
中科院分区：
文献类型：
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作者：
B. Coecke;É. O. Paquette;Dusko Pavlovic
在最近的工作中，对称匕首幺半体（SDM）类别已经成为量子力学的一种方便的分类形式化。对象代表物理系统，态射物理运算，而张量描述复合系统。经典数据与具有一些附加属性的弗罗贝尼乌斯代数相对应。它们表达了经典数据的区别能力：与量子数据相比，经典数据可以被复制和删除。因此，代数方法将经典理论的“量子化”范式转变为量子理论的“经典化”。值得注意的是，简单的 SDM 框架不仅足以满足这种概念转变，甚至允许我们区分确定性经典运算（即函数）与非确定性经典运算（即关系）以及概率性经典运算（随机映射）。此外，一些基本的分类结构（由 Kleisli 和 Grothendieck 提出）与量子态的分类表示相结合，提供了对各种量子-经典相互作用的资源敏感的解释：量子数据的经典控制，量子测量产生的经典数据，以及控制和测量之间的经典数据处理。这里的一个显着特征是分类量子力学的图形演算，它允许经典量子相互作用的纯粹图形表示。
In recent work, symmetric dagger-monoidal (SDM) categories have emerged as a convenient categorical formalization of quantum mechanics. The objects represent physical systems, the morphisms physical operations, whereas the tensors describe composite systems. Classical data turn out to correspond to Frobenius algebras with some additional properties. They express the distinguishing capabilities of classical data: in contrast with quantum data, classical data can be copied and deleted. The algebraic approach thus shifts the paradigm of ”quantization” of a classical theory to ”classicization” of a quantum theory. Remarkably, the simple SDM framework suffices not only for this conceptual shift, but even allows us to distinguish the deterministic classical operations (i.e. functions) from the nondeterministic classical operations (i.e. relations), and the probabilistic classical operations (stochastic maps). Moreover, a combination of some basic categorical constructions (due to Kleisli, resp. Grothendieck) with the categorical presentations of quantum states, provides a resource sensitive account of various quantum-classical interactions: of classical control of quantum data, of classical data arising from quantum measurements, as well as of the classical data processing inbetween controls and measurements. A salient feature here is the graphical calculus for categorical quantum mechanics, which allows a purely diagrammatic representation of classical-quantum interaction.
图解量子协议的基础
影响因子：
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作者：
Coecke B
通讯作者：
Coecke B