dorsal/arxiv
View SchemaAtemporal diagrams for quantum circuits
| Authors | Robert B. Griffiths, Shengjun Wu, Li Yu, Scott M. Cohen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507215 |
| URL | https://arxiv.org/abs/quant-ph/0507215 |
| DOI | 10.1103/PhysRevA.73.052309 |
| Journal | Physical Review A 73, 052309 (2006) |
Abstract
A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical properties to those of entangled states (map-state duality), and suggests useful analogies, such as the inverse of an entangled ket. Diagrams clarify the role of channel kets, transition operators, dynamical operators (matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite) operators are represented by diagrams with a symmetry that aids in understanding their connection with completely positive maps. The diagrams are used to analyze standard teleportation and dense coding, and for a careful study of unambiguous (conclusive) teleportation. A simple diagrammatic argument shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled using a one-qubit environment in a mixed state.
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"abstract": "A system of diagrams is introduced that allows the representation of various\nelements of a quantum circuit, including measurements, in a form which makes no\nreference to time (hence ``atemporal\u0027\u0027). It can be used to relate quantum\ndynamical properties to those of entangled states (map-state duality), and\nsuggests useful analogies, such as the inverse of an entangled ket. Diagrams\nclarify the role of channel kets, transition operators, dynamical operators\n(matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite)\noperators are represented by diagrams with a symmetry that aids in\nunderstanding their connection with completely positive maps. The diagrams are\nused to analyze standard teleportation and dense coding, and for a careful\nstudy of unambiguous (conclusive) teleportation. A simple diagrammatic argument\nshows that a Kraus rank of 3 is impossible for a one-qubit channel modeled\nusing a one-qubit environment in a mixed state.",
"arxiv_id": "quant-ph/0507215",
"authors": [
"Robert B. Griffiths",
"Shengjun Wu",
"Li Yu",
"Scott M. Cohen"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.052309",
"journal_ref": "Physical Review A 73, 052309 (2006)",
"title": "Atemporal diagrams for quantum circuits",
"url": "https://arxiv.org/abs/quant-ph/0507215"
},
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