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Qubit semantics and quantum trees

M. L. Dalla Chiara·R. Giuntini·R. Leporini·A. Leporati
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Abstract

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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M. L. Dalla Chiara, R. Giuntini, R. Leporini, A. Leporati. 2003-06-01. Qubit semantics and quantum trees. https://arxiv.org/abs/quant-ph/0211190

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