dorsal/arxiv
View SchemaFrontier between separability and quantum entanglement in a many spin system
| Authors | F. C. Alcaraz, C. Tsallis |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0110067 |
| URL | https://arxiv.org/abs/quant-ph/0110067 |
| DOI | 10.1016/S0375-9601(02)01037-X |
| Journal | Phys. Lett. A {\bf 301}, 105 (2002). |
Abstract
We discuss the critical point $x_c$ separating the quantum entangled and separable states in two series of N spins S in the simple mixed state characterized by the matrix operator $\rho=x|\tilde{\phi}><\tilde{\phi}| + \frac{1-x}{D^N} I_{D^N}$ where $x \in [0,1]$, $D =2S+1$, ${\bf I}_{D^N}$ is the $D^N \times D^N$ unity matrix and $|\tilde {\phi}>$ is a special entangled state. The cases x=0 and x=1 correspond respectively to fully random spins and to a fully entangled state. In the first of these series we consider special states $|\tilde{\phi}>$ invariant under charge conjugation, that generalizes the N=2 spin S=1/2 Einstein-Podolsky-Rosen state, and in the second one we consider generalizations of the Weber density matrices. The evaluation of the critical point $x_c$ was done through bounds coming from the partial transposition method of Peres and the conditional nonextensive entropy criterion. Our results suggest the conjecture that whenever the bounds coming from both methods coincide the result of $x_c$ is the exact one. The results we present are relevant for the discussion of quantum computing, teleportation and cryptography.
{
"annotation_id": "2870f595-eb0e-4ea1-a0b8-79cd8abbd76d",
"date_created": "2026-03-02T18:01:45.194000Z",
"date_modified": "2026-03-02T18:01:45.194000Z",
"file_hash": "cc90e149e88b3a36ad9934d8f0084043d94cf74fcf38eb00c7b4167441a62e35",
"private": false,
"record": {
"abstract": "We discuss the critical point $x_c$ separating the quantum entangled and\nseparable states in two series of N spins S in the simple mixed state\ncharacterized by the matrix operator $\\rho=x|\\tilde{\\phi}\u003e\u003c\\tilde{\\phi}| +\n\\frac{1-x}{D^N} I_{D^N}$ where $x \\in [0,1]$, $D =2S+1$, ${\\bf I}_{D^N}$ is the\n$D^N \\times D^N$ unity matrix and $|\\tilde {\\phi}\u003e$ is a special entangled\nstate. The cases x=0 and x=1 correspond respectively to fully random spins and\nto a fully entangled state. In the first of these series we consider special\nstates $|\\tilde{\\phi}\u003e$ invariant under charge conjugation, that generalizes\nthe N=2 spin S=1/2 Einstein-Podolsky-Rosen state, and in the second one we\nconsider generalizations of the Weber density matrices. The evaluation of the\ncritical point $x_c$ was done through bounds coming from the partial\ntransposition method of Peres and the conditional nonextensive entropy\ncriterion. Our results suggest the conjecture that whenever the bounds coming\nfrom both methods coincide the result of $x_c$ is the exact one. The results we\npresent are relevant for the discussion of quantum computing, teleportation and\ncryptography.",
"arxiv_id": "quant-ph/0110067",
"authors": [
"F. C. Alcaraz",
"C. Tsallis"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"cs.CC"
],
"doi": "10.1016/S0375-9601(02)01037-X",
"journal_ref": "Phys. Lett. A {\\bf 301}, 105 (2002).",
"title": "Frontier between separability and quantum entanglement in a many spin system",
"url": "https://arxiv.org/abs/quant-ph/0110067"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "777c320d-5c62-485d-833c-9608f86f4767",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}