dorsal/arxiv
View SchemaOn the Physical Interpretation of Partial Traces: Two Nonstandard Viewpoints
| Authors | Claudio Garola, Sandro Sozzo |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611072 |
| URL | https://arxiv.org/abs/quant-ph/0611072 |
| DOI | 10.1007/s11232-007-0093-1 |
| Journal | Theoretical and Mathematical Physics, 152(2): 1087-1098 (2007) |
Abstract
Mixed states are introduced in physics in order to express our ignorance about the actual state of a physical system and are represented in standard quantum mechanics (QM) by density operators. Such operators also appear if one considers a (pure) entangled state of a compound system $\Omega$ and performs partial traces on the projection operator representing it. Yet, they do not represent mixed states (or proper mixtures) of the subsystems in this case, but improper mixtures, since the coefficients in the convex sums expressing them never bear the ignorance interpretation. Hence, one cannot attribute states to the subsystems of a compound physical system in QM (subentity problem). We discuss here two alternative proposals that can be worked out within the Brussels and Lecce approaches. We firstly summarize the general framework provided by the former, which suggests that improper mixtures could be considered as new pure states. Then, we show that improper mixtures can be considered as true (yet nonpure) states also according to the latter. The two proposals seem to be compatible notwithstanding their different terminologies.
{
"annotation_id": "55f973be-9284-44ad-b295-d94feb53075e",
"date_created": "2026-03-02T18:02:30.294000Z",
"date_modified": "2026-03-02T18:02:30.294000Z",
"file_hash": "bc9085050afdb9d95124a0d348cce5466997f7fd75ba9922aeb7c4cf6b0db07a",
"private": false,
"record": {
"abstract": "Mixed states are introduced in physics in order to express our ignorance\nabout the actual state of a physical system and are represented in standard\nquantum mechanics (QM) by density operators. Such operators also appear if one\nconsiders a (pure) entangled state of a compound system $\\Omega$ and performs\npartial traces on the projection operator representing it. Yet, they do not\nrepresent mixed states (or proper mixtures) of the subsystems in this case, but\nimproper mixtures, since the coefficients in the convex sums expressing them\nnever bear the ignorance interpretation. Hence, one cannot attribute states to\nthe subsystems of a compound physical system in QM (subentity problem). We\ndiscuss here two alternative proposals that can be worked out within the\nBrussels and Lecce approaches. We firstly summarize the general framework\nprovided by the former, which suggests that improper mixtures could be\nconsidered as new pure states. Then, we show that improper mixtures can be\nconsidered as true (yet nonpure) states also according to the latter. The two\nproposals seem to be compatible notwithstanding their different terminologies.",
"arxiv_id": "quant-ph/0611072",
"authors": [
"Claudio Garola",
"Sandro Sozzo"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s11232-007-0093-1",
"journal_ref": "Theoretical and Mathematical Physics, 152(2): 1087-1098 (2007)",
"title": "On the Physical Interpretation of Partial Traces: Two Nonstandard Viewpoints",
"url": "https://arxiv.org/abs/quant-ph/0611072"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "8a9ad023-b2f9-4f70-831b-3d6304311703",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}