dorsal/arxiv
View SchemaQuantum perfect correlations and Hardy's nonlocality theorem
| Authors | Jose L. Cereceda |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9908039 |
| URL | https://arxiv.org/abs/quant-ph/9908039 |
| Journal | Found. Phys. Lett. 12 (1999) 211-231 |
Abstract
In this paper the failure of Hardy's nonlocality proof for the class of maximally entangled states is considered. A detailed analysis shows that the incompatibility of the Hardy equations for this class of states physically originates from the fact that the existence of quantum perfect correlations for the three pairs of two-valued observables (D_11,D_21), (D_11,D_22) and (D_12,D_21) [in the sense of having with certainty equal (different) readings for a joint measurement of any one of the pairs (D_11,D_21), (D_11,D_22), and (D_12,D_21)], necessarily entails perfect correlation for the pair of observables (D_12,D_22) [in the sense of having with certainty equal (different) readings for a joint measurement of the pair (D_12,D_22)]. Indeed, the set of these four perfect correlations is found to satisfy the CHSH inequality, and then no violations of local realism will arise for the maximally entangled state as far as the four observables D_ij, i,j = 1,2, are concerned. The connection between this fact and the impossibility for the quantum mechanical predictions to give the maximum possible theoretical violation of the CHSH inequality is pointed out. Moreover, it is generally proved that the fulfillment of all the Hardy nonlocality conditions necessarily entails a violation of the resulting CHSH inequality. The largest violation of this latter inequality is determined.
{
"annotation_id": "35ab7b22-d373-4722-9241-7370512491ac",
"date_created": "2026-03-02T18:02:47.440000Z",
"date_modified": "2026-03-02T18:02:47.440000Z",
"file_hash": "7a0dc90d94bc583efce3c28a6e0f753d9deeb272a5774516ff6d8fd14b7e97d5",
"private": false,
"record": {
"abstract": "In this paper the failure of Hardy\u0027s nonlocality proof for the class of\nmaximally entangled states is considered. A detailed analysis shows that the\nincompatibility of the Hardy equations for this class of states physically\noriginates from the fact that the existence of quantum perfect correlations for\nthe three pairs of two-valued observables (D_11,D_21), (D_11,D_22) and\n(D_12,D_21) [in the sense of having with certainty equal (different) readings\nfor a joint measurement of any one of the pairs (D_11,D_21), (D_11,D_22), and\n(D_12,D_21)], necessarily entails perfect correlation for the pair of\nobservables (D_12,D_22) [in the sense of having with certainty equal\n(different) readings for a joint measurement of the pair (D_12,D_22)]. Indeed,\nthe set of these four perfect correlations is found to satisfy the CHSH\ninequality, and then no violations of local realism will arise for the\nmaximally entangled state as far as the four observables D_ij, i,j = 1,2, are\nconcerned. The connection between this fact and the impossibility for the\nquantum mechanical predictions to give the maximum possible theoretical\nviolation of the CHSH inequality is pointed out. Moreover, it is generally\nproved that the fulfillment of all the Hardy nonlocality conditions necessarily\nentails a violation of the resulting CHSH inequality. The largest violation of\nthis latter inequality is determined.",
"arxiv_id": "quant-ph/9908039",
"authors": [
"Jose L. Cereceda"
],
"categories": [
"quant-ph"
],
"journal_ref": "Found. Phys. Lett. 12 (1999) 211-231",
"title": "Quantum perfect correlations and Hardy\u0027s nonlocality theorem",
"url": "https://arxiv.org/abs/quant-ph/9908039"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a6199d8b-b5b1-4f8c-8e8f-0ba8aae6d132",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}