dorsal/arxiv
View SchemaOn the geometry of a class of N-qubit entanglement monotones
| Authors | Peter Levay |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507070 |
| URL | https://arxiv.org/abs/quant-ph/0507070 |
| DOI | 10.1088/0305-4470/38/41/016 |
| Journal | Journal of Physics A38 (2005) 9075-9085 |
Abstract
A family of N-qubit entanglement monotones invariant under stochastic local operations and classical communication (SLOCC) is defined. This class of entanglement monotones includes the well-known examples of the concurrence, the three-tangle, and some of the four, five and N-qubit SLOCC invariants introduced recently. The construction of these invariants is based on bipartite partitions of the Hilbert space in the form ${\bf C}^{2^N}\simeq{\bf C}^L\otimes{\bf C}^l$ with $L=2^{N-n}\geq l=2^n$. Such partitions can be given a nice geometrical interpretation in terms of Grassmannians Gr(L,l) of l-planes in ${\bf C}^L$ that can be realized as the zero locus of quadratic polinomials in the complex projective space of suitable dimension via the Plucker embedding. The invariants are neatly expressed in terms of the Plucker coordinates of the Grassmannian.
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"abstract": "A family of N-qubit entanglement monotones invariant under stochastic local\noperations and classical communication (SLOCC) is defined. This class of\nentanglement monotones includes the well-known examples of the concurrence, the\nthree-tangle, and some of the four, five and N-qubit SLOCC invariants\nintroduced recently. The construction of these invariants is based on bipartite\npartitions of the Hilbert space in the form ${\\bf C}^{2^N}\\simeq{\\bf\nC}^L\\otimes{\\bf C}^l$ with $L=2^{N-n}\\geq l=2^n$. Such partitions can be given\na nice geometrical interpretation in terms of Grassmannians Gr(L,l) of l-planes\nin ${\\bf C}^L$ that can be realized as the zero locus of quadratic polinomials\nin the complex projective space of suitable dimension via the Plucker\nembedding. The invariants are neatly expressed in terms of the Plucker\ncoordinates of the Grassmannian.",
"arxiv_id": "quant-ph/0507070",
"authors": [
"Peter Levay"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/38/41/016",
"journal_ref": "Journal of Physics A38 (2005) 9075-9085",
"title": "On the geometry of a class of N-qubit entanglement monotones",
"url": "https://arxiv.org/abs/quant-ph/0507070"
},
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