dorsal/arxiv
View SchemaExistence of the Schmidt decomposition for tripartite systems
| Authors | Arun K. Pati |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9911073 |
| URL | https://arxiv.org/abs/quant-ph/9911073 |
| DOI | 10.1016/S0375-9601(00)00767-2 |
Abstract
For any bipartite quantum system the Schmidt decomposition allows us to express the state vector in terms of a single sum instead of double sums. We show the existence of the Schmidt decomposition for tripartite system under certain condition. If the partial inner product of a basis (belonging to a Hilbert space of smaller dimension) with the state of the composite system gives a disentangled basis, then the Schmidt decomposition for a tripartite system exists. In this case the reduced density matrix of each of the subsystem has equal spectrum in the Schmidt basis.
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"abstract": "For any bipartite quantum system the Schmidt decomposition allows us to\nexpress the state vector in terms of a single sum instead of double sums. We\nshow the existence of the Schmidt decomposition for tripartite system under\ncertain condition. If the partial inner product of a basis (belonging to a\nHilbert space of smaller dimension) with the state of the composite system\ngives a disentangled basis, then the Schmidt decomposition for a tripartite\nsystem exists. In this case the reduced density matrix of each of the subsystem\nhas equal spectrum in the Schmidt basis.",
"arxiv_id": "quant-ph/9911073",
"authors": [
"Arun K. Pati"
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"categories": [
"quant-ph"
],
"doi": "10.1016/S0375-9601(00)00767-2",
"title": "Existence of the Schmidt decomposition for tripartite systems",
"url": "https://arxiv.org/abs/quant-ph/9911073"
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