dorsal/arxiv
View SchemaSymmetry implies independence
| Authors | Renato Renner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0703069 |
| URL | https://arxiv.org/abs/quant-ph/0703069 |
| DOI | 10.1038/nphys684 |
| Journal | Nature Physics 3, 645 - 649 (2007) |
Abstract
Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other. This result generalises de Finetti's classical representation theorem for infinitely exchangeable sequences of random variables as well as its quantum-mechanical analogue. It has applications in various areas of physics as well as information theory and cryptography. For example, in experimental physics, one typically collects data by running a certain experiment many times, assuming that the individual runs are mutually independent. Our result can be used to justify this assumption.
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"abstract": "Given a quantum system consisting of many parts, we show that symmetry of the\nsystem\u0027s state, i.e., invariance under swappings of the subsystems, implies\nthat almost all of its parts are virtually identical and independent of each\nother. This result generalises de Finetti\u0027s classical representation theorem\nfor infinitely exchangeable sequences of random variables as well as its\nquantum-mechanical analogue. It has applications in various areas of physics as\nwell as information theory and cryptography. For example, in experimental\nphysics, one typically collects data by running a certain experiment many\ntimes, assuming that the individual runs are mutually independent. Our result\ncan be used to justify this assumption.",
"arxiv_id": "quant-ph/0703069",
"authors": [
"Renato Renner"
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"doi": "10.1038/nphys684",
"journal_ref": "Nature Physics 3, 645 - 649 (2007)",
"title": "Symmetry implies independence",
"url": "https://arxiv.org/abs/quant-ph/0703069"
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