dorsal/arxiv
View SchemaQuantum information-flow, concretely, and axiomatically
| Authors | Bob Coecke |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506132 |
| URL | https://arxiv.org/abs/quant-ph/0506132 |
| DOI | 10.1117/12.620297 |
Abstract
These lecture notes survey some joint work with Samson Abramsky. Somewhat informally I will discuss the main results in a pedestrian not too technical way. These include: (1) `The logic of entanglement', that is, the identification and abstract axiomatization of the `quantum information-flow' which enables protocols such as quantum teleportation. To this means we define strongly compact closed categories which abstractly capture the behavioral properties of quantum entanglement. (2) `Postulates for an abstract quantum formalism' in which classical information-flow (e.g. token exchange) is part of the formalism. As an example, we provide a purely formal description of quantum teleportation and prove correctness in abstract generality. In this formalism types reflect kinds, contra the essentially typeless von Neumann formalism. Hence even concretely this formalism manifestly improves on the usual one. (3) `A high-level approach to quantum informatics'.
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"abstract": "These lecture notes survey some joint work with Samson Abramsky. Somewhat\ninformally I will discuss the main results in a pedestrian not too technical\nway. These include: (1) `The logic of entanglement\u0027, that is, the\nidentification and abstract axiomatization of the `quantum information-flow\u0027\nwhich enables protocols such as quantum teleportation. To this means we define\nstrongly compact closed categories which abstractly capture the behavioral\nproperties of quantum entanglement. (2) `Postulates for an abstract quantum\nformalism\u0027 in which classical information-flow (e.g. token exchange) is part of\nthe formalism. As an example, we provide a purely formal description of quantum\nteleportation and prove correctness in abstract generality. In this formalism\ntypes reflect kinds, contra the essentially typeless von Neumann formalism.\nHence even concretely this formalism manifestly improves on the usual one. (3)\n`A high-level approach to quantum informatics\u0027.",
"arxiv_id": "quant-ph/0506132",
"authors": [
"Bob Coecke"
],
"categories": [
"quant-ph",
"math.CT",
"math.LO"
],
"doi": "10.1117/12.620297",
"title": "Quantum information-flow, concretely, and axiomatically",
"url": "https://arxiv.org/abs/quant-ph/0506132"
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