dorsal/arxiv
View SchemaUncertainty, Monogamy, and Locking of Quantum Correlations
| Authors | Matthias Christandl, Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0501090 |
| URL | https://arxiv.org/abs/quant-ph/0501090 |
| DOI | 10.1109/TIT.2005.853338 |
| Journal | IEEE Trans Inf Theory, vol 51, no 9, pp 3159-3165 (2005). |
Abstract
Squashed entanglement and entanglement of purification are quantum mechanical correlation measures and defined as certain minimisations of entropic quantities. We present the first non-trivial calculations of both quantities. Our results lead to the conclusion that both measures can drop by an arbitrary amount when only a single qubit of a local system is lost. This property is known as "locking" and has previously been observed for other correlation measures, such as the accessible information, entanglement cost and the logarithmic negativity. In the case of squashed entanglement, the results are obtained with the help of an inequality that can be understood as a quantum channel analogue of well-known entropic uncertainty relations. This inequality may prove a useful tool in quantum information theory. The regularised entanglement of purification is known to equal the entanglement needed to prepare a many copies of quantum state by local operations and a sublinear amount of communication. Here, monogamy of quantum entanglement (i.e., the impossibility of a system being maximally entangled with two others at the same time) leads to an exact calculation for all quantum states that are supported either on the symmetric or on the antisymmetric subspace of a dxd-dimensional system.
{
"annotation_id": "53f0f5ef-a839-41e5-95b4-15c75428e1f7",
"date_created": "2026-03-02T18:02:13.508000Z",
"date_modified": "2026-03-02T18:02:13.508000Z",
"file_hash": "c42417c241d2eb391eb5d947ab72bb8a3b24f32ecc5169759682dc3bab13ea3f",
"private": false,
"record": {
"abstract": "Squashed entanglement and entanglement of purification are quantum mechanical\ncorrelation measures and defined as certain minimisations of entropic\nquantities. We present the first non-trivial calculations of both quantities.\nOur results lead to the conclusion that both measures can drop by an arbitrary\namount when only a single qubit of a local system is lost. This property is\nknown as \"locking\" and has previously been observed for other correlation\nmeasures, such as the accessible information, entanglement cost and the\nlogarithmic negativity.\n In the case of squashed entanglement, the results are obtained with the help\nof an inequality that can be understood as a quantum channel analogue of\nwell-known entropic uncertainty relations. This inequality may prove a useful\ntool in quantum information theory.\n The regularised entanglement of purification is known to equal the\nentanglement needed to prepare a many copies of quantum state by local\noperations and a sublinear amount of communication. Here, monogamy of quantum\nentanglement (i.e., the impossibility of a system being maximally entangled\nwith two others at the same time) leads to an exact calculation for all quantum\nstates that are supported either on the symmetric or on the antisymmetric\nsubspace of a dxd-dimensional system.",
"arxiv_id": "quant-ph/0501090",
"authors": [
"Matthias Christandl",
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"doi": "10.1109/TIT.2005.853338",
"journal_ref": "IEEE Trans Inf Theory, vol 51, no 9, pp 3159-3165 (2005).",
"title": "Uncertainty, Monogamy, and Locking of Quantum Correlations",
"url": "https://arxiv.org/abs/quant-ph/0501090"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "37ad32e0-f3f9-4916-80d5-7e4e266bb374",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}