dorsal/arxiv
View SchemaCombinatorial approach to multipartite quantum systems:basic formulation
| Authors | Ali Saif M. Hassan, Pramod Joag |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602053 |
| URL | https://arxiv.org/abs/quant-ph/0602053 |
| DOI | 10.1088/1751-8113/40/33/019 |
| Journal | J. Phys. A: Math. Theor. 40 (2007) 10251--10290 |
Abstract
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of pure and mixed states, Von-Neumann entropy, separability of multipartite quantum states and quantum operations in terms of the graphs associated with quantum states. In order to address the separability and entanglement questions using graphs, we introduce a modified tensor product of weighted graphs, and establish its algebraic properties. In particular, we show that Werner's definition [1] of a separable state can be written in terms of a graphs, for the states in a real or complex Hilbert space. We generalize the separability criterion (degree criterion) due to S.L. Braunstein, S. Ghosh, T. Mansour, S. Severini, R.C. Wilson [2], to a class of weighted graphs with real weights. We have given some criteria for the Laplacian associated with a weighted graph to be positive semidefinite.
{
"annotation_id": "1a98d7ba-0011-4a50-9a87-059b1d0903f1",
"date_created": "2026-03-02T18:02:23.615000Z",
"date_modified": "2026-03-02T18:02:23.615000Z",
"file_hash": "cf5a62988613d29f61baeef9e6547dfcab634199105740770a80af1526b1e30a",
"private": false,
"record": {
"abstract": "In this paper we give a method to associate a graph with an arbitrary density\nmatrix referred to a standard orthonormal basis in the Hilbert space of a\nfinite dimensional quantum system. We study the related issues like\nclassification of pure and mixed states, Von-Neumann entropy, separability of\nmultipartite quantum states and quantum operations in terms of the graphs\nassociated with quantum states. In order to address the separability and\nentanglement questions using graphs, we introduce a modified tensor product of\nweighted graphs, and establish its algebraic properties. In particular, we show\nthat Werner\u0027s definition [1] of a separable state can be written in terms of a\ngraphs, for the states in a real or complex Hilbert space. We generalize the\nseparability criterion (degree criterion) due to S.L. Braunstein, S. Ghosh, T.\nMansour, S. Severini, R.C. Wilson [2], to a class of weighted graphs with real\nweights. We have given some criteria for the Laplacian associated with a\nweighted graph to be positive semidefinite.",
"arxiv_id": "quant-ph/0602053",
"authors": [
"Ali Saif M. Hassan",
"Pramod Joag"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1751-8113/40/33/019",
"journal_ref": "J. Phys. A: Math. Theor. 40 (2007) 10251--10290",
"title": "Combinatorial approach to multipartite quantum systems:basic formulation",
"url": "https://arxiv.org/abs/quant-ph/0602053"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "90ab85f5-49de-4a6d-bd40-e4e1d8261103",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}