dorsal/arxiv
View SchemaThe Born rule from a consistency requirement on hidden measurements in complex Hilbert space
| Authors | S. Aerts |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0212151 |
| URL | https://arxiv.org/abs/quant-ph/0212151 |
Abstract
We formalize the hidden measurement approach within the very general notion of an interactive probability model. We narrow down the model by assuming the state space of a physical entity is a complex Hilbert space and introduce the principle of consistent interaction which effectively partitions the space of apparatus states. The normalized measure of the set of apparatus states that interact with a pure state giving rise to a fixed outcome is shown to be in accordance with the probability obtained using the Born rule.
{
"annotation_id": "b9e96342-a7fc-422c-ac00-fddb2da55ae4",
"date_created": "2026-03-02T18:01:56.194000Z",
"date_modified": "2026-03-02T18:01:56.194000Z",
"file_hash": "1e10b3cfa5e32a1500f684a7194c89ab17684a52811105fab84e1b5f33a8af75",
"private": false,
"record": {
"abstract": "We formalize the hidden measurement approach within the very general notion\nof an interactive probability model. We narrow down the model by assuming the\nstate space of a physical entity is a complex Hilbert space and introduce the\nprinciple of consistent interaction which effectively partitions the space of\napparatus states. The normalized measure of the set of apparatus states that\ninteract with a pure state giving rise to a fixed outcome is shown to be in\naccordance with the probability obtained using the Born rule.",
"arxiv_id": "quant-ph/0212151",
"authors": [
"S. Aerts"
],
"categories": [
"quant-ph"
],
"title": "The Born rule from a consistency requirement on hidden measurements in complex Hilbert space",
"url": "https://arxiv.org/abs/quant-ph/0212151"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "eccc47d4-7b90-4efc-8731-36704c949ae0",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}