dorsal/arxiv
View SchemaLocal copying of orthogonal entangled quantum states
| Authors | Fabio Anselmi, Anthony Chefles, Martin B. Plenio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407168 |
| URL | https://arxiv.org/abs/quant-ph/0407168 |
| DOI | 10.1088/1367-2630/6/1/164 |
Abstract
In classical information theory one can, in principle, produce a perfect copy of any input state. In quantum information theory, the no cloning theorem prohibits exact copying of nonorthogonal states. Moreover, if we wish to copy multiparticle entangled states and can perform only local operations and classical communication (LOCC), then further restrictions apply. We investigate the problem of copying orthogonal, entangled quantum states with an entangled blank state under the restriction to LOCC. Throughout, the subsystems have finite dimension D. We show that if all of the states to be copied are non-maximally entangled, then novel LOCC copying procedures based on entanglement catalysis are possible. We then study in detail the LOCC copying problem where both the blank state and at least one of the states to be copied are maximally entangled. For this to be possible, we find that all the states to be copied must be maximally entangled. We obtain a necessary and sufficient condition for LOCC copying under these conditions. For two orthogonal, maximally entangled states, we provide the general solution to this condition. We use it to show that for D=2,3, any pair of orthogonal, maximally entangled states can be locally copied using a maximally entangled blank state. However, we also show that for any D which is not prime, one can construct pairs of such states for which this is impossible.
{
"annotation_id": "b1c40113-947b-474c-89e1-537033fa2a55",
"date_created": "2026-03-02T18:02:10.182000Z",
"date_modified": "2026-03-02T18:02:10.182000Z",
"file_hash": "6b8d4dce4ada9aab0a104bdf1909a25fb36bdc3d5b494f14887bf151471dbb6f",
"private": false,
"record": {
"abstract": "In classical information theory one can, in principle, produce a perfect copy\nof any input state. In quantum information theory, the no cloning theorem\nprohibits exact copying of nonorthogonal states. Moreover, if we wish to copy\nmultiparticle entangled states and can perform only local operations and\nclassical communication (LOCC), then further restrictions apply. We investigate\nthe problem of copying orthogonal, entangled quantum states with an entangled\nblank state under the restriction to LOCC. Throughout, the subsystems have\nfinite dimension D. We show that if all of the states to be copied are\nnon-maximally entangled, then novel LOCC copying procedures based on\nentanglement catalysis are possible. We then study in detail the LOCC copying\nproblem where both the blank state and at least one of the states to be copied\nare maximally entangled. For this to be possible, we find that all the states\nto be copied must be maximally entangled. We obtain a necessary and sufficient\ncondition for LOCC copying under these conditions. For two orthogonal,\nmaximally entangled states, we provide the general solution to this condition.\nWe use it to show that for D=2,3, any pair of orthogonal, maximally entangled\nstates can be locally copied using a maximally entangled blank state. However,\nwe also show that for any D which is not prime, one can construct pairs of such\nstates for which this is impossible.",
"arxiv_id": "quant-ph/0407168",
"authors": [
"Fabio Anselmi",
"Anthony Chefles",
"Martin B. Plenio"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1367-2630/6/1/164",
"title": "Local copying of orthogonal entangled quantum states",
"url": "https://arxiv.org/abs/quant-ph/0407168"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "7bdcef7e-4411-4765-bafd-3cba28764bdf",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}