dorsal/arxiv
View SchemaComplementarity relations for multi-qubit systems
| Authors | Tracey E. Tessier |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403022 |
| URL | https://arxiv.org/abs/quant-ph/0403022 |
| DOI | 10.1007/s10702-005-3956-4 |
| Journal | Found. Phys. Lett. 18(2), 107 (2005) |
Abstract
We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the degree to which single particle properties are possessed by an individual member of the system is limited by the bipartite entanglement that exists between that qubit and the remainder of the system. This result implies that the phenomenon of entanglement sharing is one specific consequence of complementarity. The second expression, which holds for an arbitrary state of two qubits, pure or mixed, quantifies a tradeoff between the amounts of entanglement, separable uncertainty, and single particle properties that are encoded in the quantum state. The separable uncertainty is a natural measure of our ignorance about the properties possessed by individual subsystems, and may be used to completely characterize the relationship between entanglement and mixedness in two-qubit systems. The two-qubit complementarity relation yields a useful geometric picture in which the root mean square values of local subsystem properties act like coordinates in the space of density matrices, and suggests possible insights into the problem of interpreting quantum mechanics.
{
"annotation_id": "9ed45220-a3ae-4cc9-9cf6-bb702a4e4f57",
"date_created": "2026-03-02T18:02:06.505000Z",
"date_modified": "2026-03-02T18:02:06.505000Z",
"file_hash": "e454c986b8dd4737bac9c81050657b3a5013336ed52e0f3cef38cbb18d8259aa",
"private": false,
"record": {
"abstract": "We derive two complementarity relations that constrain the individual and\nbipartite properties that may simultaneously exist in a multi-qubit system. The\nfirst expression, valid for an arbitrary pure state of n qubits, demonstrates\nthat the degree to which single particle properties are possessed by an\nindividual member of the system is limited by the bipartite entanglement that\nexists between that qubit and the remainder of the system. This result implies\nthat the phenomenon of entanglement sharing is one specific consequence of\ncomplementarity. The second expression, which holds for an arbitrary state of\ntwo qubits, pure or mixed, quantifies a tradeoff between the amounts of\nentanglement, separable uncertainty, and single particle properties that are\nencoded in the quantum state. The separable uncertainty is a natural measure of\nour ignorance about the properties possessed by individual subsystems, and may\nbe used to completely characterize the relationship between entanglement and\nmixedness in two-qubit systems. The two-qubit complementarity relation yields a\nuseful geometric picture in which the root mean square values of local\nsubsystem properties act like coordinates in the space of density matrices, and\nsuggests possible insights into the problem of interpreting quantum mechanics.",
"arxiv_id": "quant-ph/0403022",
"authors": [
"Tracey E. Tessier"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s10702-005-3956-4",
"journal_ref": "Found. Phys. Lett. 18(2), 107 (2005)",
"title": "Complementarity relations for multi-qubit systems",
"url": "https://arxiv.org/abs/quant-ph/0403022"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "af8c7028-bc8b-4299-a74a-47e33d8329b6",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}