dorsal/arxiv
View SchemaOn the one-particle reduced density matrices of a pure three-qutrit quantum state
| Authors | Atsushi Higuchi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0309186 |
| URL | https://arxiv.org/abs/quant-ph/0309186 |
Abstract
We present a necessary and sufficient condition for three qutrit density matrices to be the one-particle reduced density matrices of a pure three-qutrit quantum state. The condition consists of seven classes of inequalities satisfied by the eigenvalues of these matrices. One of them is a generalization of a known inequality for the qubit case. Some of these inequalities are proved algebraically whereas the proof of the others uses the fact that a continuous function of the state must have a minimum. Construction of states satisfying these inequalities relies on a representation of the convex set of the allowed set of eigenvalues in terms of corner points. We also present a result for a more general quantum system concerning the nature of the boundary surface of the set of the allowed set of eigenvalues.
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"abstract": "We present a necessary and sufficient condition for three qutrit density\nmatrices to be the one-particle reduced density matrices of a pure three-qutrit\nquantum state. The condition consists of seven classes of inequalities\nsatisfied by the eigenvalues of these matrices. One of them is a generalization\nof a known inequality for the qubit case. Some of these inequalities are proved\nalgebraically whereas the proof of the others uses the fact that a continuous\nfunction of the state must have a minimum. Construction of states satisfying\nthese inequalities relies on a representation of the convex set of the allowed\nset of eigenvalues in terms of corner points. We also present a result for a\nmore general quantum system concerning the nature of the boundary surface of\nthe set of the allowed set of eigenvalues.",
"arxiv_id": "quant-ph/0309186",
"authors": [
"Atsushi Higuchi"
],
"categories": [
"quant-ph"
],
"title": "On the one-particle reduced density matrices of a pure three-qutrit quantum state",
"url": "https://arxiv.org/abs/quant-ph/0309186"
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