Quantum and Classical Structures in Nondeterminstic Computation
Quantum and Classical Structures in Nondeterminstic Computation
复制标题
非确定性计算中的量子和经典结构
DOI：
10.1007/978-3-642-00834-4_13
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发表时间：
2008
影响因子：
4.1
通讯作者：
Dusko Pavlovic
中科院分区：
文献类型：
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作者：
Dusko Pavlovic
在分类量子力学中，经典结构一方面表征了量子资源的经典界面，另一方面又引发了一些量子现象。在量子理论的标准希尔伯特空间模型中，空间上的经典结构与其正交基相对应。在本文中，我们证明关系范畴中的经典结构对应于交换群的直和。当然，虽然关系不是一个有趣的量子计算模型，但这个结果有一些有趣的计算解释。如果关系被视为非确定性程序的表示，那么它就会在这个熟悉的经典计算领域中揭示出各种各样的非标准量子结构。具有讽刺意味的是，它还开辟了量子力学哲学中所谓的本体认知差距的一个版本，因为它没有为这些非标准量子结构提供接口。
In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard Hilbert space model of quantum theories, classical structures over a space correspond to its orthonormal bases. In the present paper, we show that classical structures in the category of relations correspond to direct sums of abelian groups. Although relations are, of course, not an interesting model of quantum computation, this result has some interesting computational interpretations. If relations are viewed as denotations of nondeterministic programs, it uncovers a wide variety of non-standard quantum structures in this familiar area of classical computation. Ironically, it also opens up a version of what in philosophy of quantum mechanics would be called an ontic-epistemic gap, as it provides no interface to these nonstandard quantum structures.