dorsal/arxiv
View SchemaThe Spectra of Density Operators and the Kronecker Coefficients of the Symmetric Group
| Authors | Matthias Christandl, Graeme Mitchison |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409016 |
| URL | https://arxiv.org/abs/quant-ph/0409016 |
| DOI | 10.1007/s00220-005-1435-1 |
| Journal | Commun. Math. Phys., Vol. 261, No. 3, pp. 789-797 (2006) |
Abstract
Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can associate a representation of the symmetric group defined by a Young diagram whose normalised row lengths approximate the spectrum. We show that, for allowed spectra, the representation of the composite system is contained in the tensor product of the representations of the two subsystems. This gives a new physical meaning to representations of the symmetric group. It also introduces a new way of using the machinery of group theory in quantum informational problems, which we illustrate by two simple examples.
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"abstract": "Determining the relationship between composite systems and their subsystems\nis a fundamental problem in quantum physics. In this paper we consider the\nspectra of a bipartite quantum state and its two marginal states. To each\nspectrum we can associate a representation of the symmetric group defined by a\nYoung diagram whose normalised row lengths approximate the spectrum. We show\nthat, for allowed spectra, the representation of the composite system is\ncontained in the tensor product of the representations of the two subsystems.\nThis gives a new physical meaning to representations of the symmetric group. It\nalso introduces a new way of using the machinery of group theory in quantum\ninformational problems, which we illustrate by two simple examples.",
"arxiv_id": "quant-ph/0409016",
"authors": [
"Matthias Christandl",
"Graeme Mitchison"
],
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"quant-ph"
],
"doi": "10.1007/s00220-005-1435-1",
"journal_ref": "Commun. Math. Phys., Vol. 261, No. 3, pp. 789-797 (2006)",
"title": "The Spectra of Density Operators and the Kronecker Coefficients of the Symmetric Group",
"url": "https://arxiv.org/abs/quant-ph/0409016"
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