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arXiv quant-ph/0611119quant-phhep-thmath.LO
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基本逻辑与量子纠缠

Basic Logic and Quantum Entanglement

Paola Zizzi

摘要:

众所周知,量子纠缠是量子计算最重要的特征之一,因为它导致大规模的量子并行性,从而使计算速度呈指数级提高。从某种意义上说,量子纠缠被认为是量子计算本身的一种隐含性质。但是...可否说得清楚一点?换句话说,是否有可能在机器语言的逻辑微积分中找到连接符“纠缠”?还有,有没有可能“教”量子计算机“模仿”EPR“悖论”?答案是肯定的,如果逻辑微积分是最弱的可能逻辑,即基本逻辑。弱逻辑几乎没有结构规则。但在逻辑中,弱结构为连接词留下了更多的空间(例如连接词“纠缠”)。此外,在基本逻辑中,压缩和弱化这两个结构规则的缺失分别对应于量子计算中的不可克隆定理和不可擦除定理的有效性。

英文摘要:

As it is well known, quantum entanglement is one of the most important features of quantum computing, as it leads to massive quantum parallelism, hence to exponential computational speed-up. In a sense, quantum entanglement is considered as an implicit property of quantum computation itself. But...can it be made explicit? In other words, is it possible to find the connective "entanglement" in a logical sequent calculus for the machine language? And also, is it possible to "teach" the quantum computer to "mimic" the EPR "paradox"? The answer is in the affirmative, if the logical sequent calculus is that of the weakest possible logic, namely Basic logic. A weak logic has few structural rules. But in logic, a weak structure leaves more room for connectives (for example the connective "entanglement"). Furthermore, the absence in Basic logic of the two structural rules of contraction and weakening corresponds to the validity of the no-cloning and no-erase theorems, respectively, in quantum computing.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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