dorsal/arxiv
View SchemaReflection Symmetries for Multiqubit Density Operators
| Authors | Claudio Altafini, Timothy F. Havel |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0405123 |
| URL | https://arxiv.org/abs/quant-ph/0405123 |
| DOI | 10.1063/1.2181827 |
| Journal | Journal of Mathematical Physics, 47, 032104, 2006 |
Abstract
For multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.e., orientation changing rotations. While one-qubit reflections correspond to antiunitary symmetries, as is known for example from the partial transposition criterion, reflections on the joint density of two or more qubits are not accounted for by the Wigner Theorem and are well-posed only for sufficiently mixed states. One example of such nonlocal reflections is the unconditional NOT operation on a multiparty density, i.e., an operation yelding another density and such that the sum of the two is the identity operator. This nonphysical operation is admissible only for sufficiently mixed states.
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"abstract": "For multiqubit density operators in a suitable tensorial basis, we show that\na number of nonunitary operations used in the detection and synthesis of\nentanglement are classifiable as reflection symmetries, i.e., orientation\nchanging rotations. While one-qubit reflections correspond to antiunitary\nsymmetries, as is known for example from the partial transposition criterion,\nreflections on the joint density of two or more qubits are not accounted for by\nthe Wigner Theorem and are well-posed only for sufficiently mixed states. One\nexample of such nonlocal reflections is the unconditional NOT operation on a\nmultiparty density, i.e., an operation yelding another density and such that\nthe sum of the two is the identity operator. This nonphysical operation is\nadmissible only for sufficiently mixed states.",
"arxiv_id": "quant-ph/0405123",
"authors": [
"Claudio Altafini",
"Timothy F. Havel"
],
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"quant-ph"
],
"doi": "10.1063/1.2181827",
"journal_ref": "Journal of Mathematical Physics, 47, 032104, 2006",
"title": "Reflection Symmetries for Multiqubit Density Operators",
"url": "https://arxiv.org/abs/quant-ph/0405123"
},
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