dorsal/arxiv
View SchemaTowards a geometrical interpretation of quantum information compression
| Authors | Graeme Mitchison, Richard Jozsa |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0309177 |
| URL | https://arxiv.org/abs/quant-ph/0309177 |
| DOI | 10.1103/PhysRevA.69.032304 |
Abstract
Let S be the von Neumann entropy of a finite ensemble E of pure quantum states. We show that S may be naturally viewed as a function of a set of geometrical volumes in Hilbert space defined by the states and that S is monotonically increasing in each of these variables. Since S is the Schumacher compression limit of E, this monotonicity property suggests a geometrical interpretation of the quantum redundancy involved in the compression process. It provides clarification of previous work in which it was shown that S may be increased while increasing the overlap of each pair of states in the ensemble. As a byproduct, our mathematical techniques also provide a new interpretation of the subentropy of E.
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"abstract": "Let S be the von Neumann entropy of a finite ensemble E of pure quantum\nstates. We show that S may be naturally viewed as a function of a set of\ngeometrical volumes in Hilbert space defined by the states and that S is\nmonotonically increasing in each of these variables. Since S is the Schumacher\ncompression limit of E, this monotonicity property suggests a geometrical\ninterpretation of the quantum redundancy involved in the compression process.\nIt provides clarification of previous work in which it was shown that S may be\nincreased while increasing the overlap of each pair of states in the ensemble.\nAs a byproduct, our mathematical techniques also provide a new interpretation\nof the subentropy of E.",
"arxiv_id": "quant-ph/0309177",
"authors": [
"Graeme Mitchison",
"Richard Jozsa"
],
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"quant-ph"
],
"doi": "10.1103/PhysRevA.69.032304",
"title": "Towards a geometrical interpretation of quantum information compression",
"url": "https://arxiv.org/abs/quant-ph/0309177"
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