dorsal/arxiv
View SchemaQubit semantics and quantum trees
| Authors | M. L. Dalla Chiara, R. Giuntini, R. Leporini, A. Leporati |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211190 |
| URL | https://arxiv.org/abs/quant-ph/0211190 |
Abstract
In the qubit semantics the \emph{meaning} of any sentence $\alpha$ 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 $\alpha$. 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 $\alpha$ gives rise to a \emph{quantum tree}, consisting of a sequence of unitary operators. The quantum tree of $\alpha$ can be regarded as a quantum circuit that transforms the quregister associated to the atomic subformulas of $\alpha$ into the quregster associated to $\alpha$.
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"abstract": "In the qubit semantics the \\emph{meaning} of any sentence $\\alpha$ is\nrepresented by a \\emph{quregister}: a unit vector of the $n$--fold tensor\nproduct $\\otimes^n \\C^2$, where $n$ depends on the number of occurrences of\natomic sentences in $\\alpha$. The logic characterized by this semantics, called\n{\\it quantum computational logic} (QCL), is {\\it unsharp}, because the\nnon-contradiction principle is violated. We show that QCL does not admit any\nlogical truth. In this framework, any sentence $\\alpha$ gives rise to a\n\\emph{quantum tree}, consisting of a sequence of unitary operators. The quantum\ntree of $\\alpha$ can be regarded as a quantum circuit that transforms the\nquregister associated to the atomic subformulas of $\\alpha$ into the quregster\nassociated to $\\alpha$.",
"arxiv_id": "quant-ph/0211190",
"authors": [
"M. L. Dalla Chiara",
"R. Giuntini",
"R. Leporini",
"A. Leporati"
],
"categories": [
"quant-ph"
],
"title": "Qubit semantics and quantum trees",
"url": "https://arxiv.org/abs/quant-ph/0211190"
},
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