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arXiv quant-ph/0211190quant-ph
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量子比特语义和量子树

Qubit semantics and quantum trees

M. L. Dalla Chiara, R. Giuntini, R. Leporini, A. Leporati

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10 pages, 2 figures
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摘要：

在量子位语义中，任何句子$α$的\emph{meaning}都由\emph{quregister}表示：$n$ -倍张量积$\otimes^n \C^2$的单位向量，其中$n$取决于$α$中原子句子的出现次数。由这种语义表征的逻辑，称为{ \it量子计算逻辑}（QCL），是{ \it unsharp}，因为违反了非矛盾原则。我们表明，QCL不承认任何逻辑真理。在这个框架中，任何句子$α$都会产生一个\emph{quantum tree}，它由一系列酉算子组成。$α$的量子树可以被认为是将与$α$的原子子公式相关联的quregister转换为与$α$相关联的quregster的量子线路。

英文摘要：

In the qubit semantics the \emph{meaning} of any sentence $α$ is represented by a \emph{quregister}: a unit vector of the $n$--fold tensor product $\otimes^n \C^2$, where $n$ depends on the number of occurrences of atomic sentences in $α$. The logic characterized by this semantics, called {\it quantum computational logic} (QCL), is {\it unsharp}, because the non-contradiction principle is violated. We show that QCL does not admit any logical truth. In this framework, any sentence $α$ gives rise to a \emph{quantum tree}, consisting of a sequence of unitary operators. The quantum tree of $α$ can be regarded as a quantum circuit that transforms the quregister associated to the atomic subformulas of $α$ into the quregster associated to $α$.

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