dorsal/arxiv
View SchemaInformation and Distinguishability of Ensembles of Identical Quantum States
| Authors | Lev B. Levitin, Tommaso Toffoli, Zac D. Walton |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112075 |
| URL | https://arxiv.org/abs/quant-ph/0112075 |
Abstract
We consider a fixed quantum measurement performed over $n$ identical copies of quantum states. Using a rigorous notion of distinguishability We consider a fixed quantum measurement performed over $n$ identical copies of quantum states. Using a rigorous notion of distinguishability based on Shannon's 12th theorem, we show that in the case of a single qubit the number of distinguishable states is $W(\alpha_1,\alpha_2,n)=|\alpha_1-\alpha_2|\sqrt{\frac{2n}{\pi e}}$, where $(\alpha_1,\alpha_2)$ is the angle interval from which the states are chosen. In the general case of an $N$-dimensional Hilbert space and an area $\Omega$ of the domain on the unit sphere from which the states are chosen, the number of distinguishable states is $W(N,n,\Omega)=\Omega(\frac{2n}{\pi e})^{\frac{N-1}{2}}$. The optimal distribution is uniform over the domain in Cartesian coordinates.based on Shannon's 12th theorem, we show that in the case of a single qubit the number of distinguishable states is $W(\alpha_1,\alpha_2,n)=|\alpha_1-\alpha_2|\sqrt{\frac{2n}{\pi e}}$, where $(\alpha_1,\alpha_2)$ is the angle interval from which the states are chosen. In the general case of an $N$-dimensional Hilbert space and an area $\Omega$ of the domain on the unit sphere from which the states are chosen, the number of distinguishable states is $W(N,n,\Omega)=\Omega(\frac{2n}{\pi e})^{\frac{N-1}{2}}$. The optimal distribution is uniform over the domain in Cartesian coordinates.
{
"annotation_id": "fd5ab942-c16c-4394-9b92-6734ba843188",
"date_created": "2026-03-02T18:01:49.009000Z",
"date_modified": "2026-03-02T18:01:49.009000Z",
"file_hash": "61c505d1e8390bef14025fc7055ccc39097ca89224d25762353b005bb4e5fe54",
"private": false,
"record": {
"abstract": "We consider a fixed quantum measurement performed over $n$ identical copies\nof quantum states. Using a rigorous notion of distinguishability We consider a\nfixed quantum measurement performed over $n$ identical copies of quantum\nstates. Using a rigorous notion of distinguishability based on Shannon\u0027s 12th\ntheorem, we show that in the case of a single qubit the number of\ndistinguishable states is\n$W(\\alpha_1,\\alpha_2,n)=|\\alpha_1-\\alpha_2|\\sqrt{\\frac{2n}{\\pi e}}$, where\n$(\\alpha_1,\\alpha_2)$ is the angle interval from which the states are chosen.\nIn the general case of an $N$-dimensional Hilbert space and an area $\\Omega$ of\nthe domain on the unit sphere from which the states are chosen, the number of\ndistinguishable states is $W(N,n,\\Omega)=\\Omega(\\frac{2n}{\\pi\ne})^{\\frac{N-1}{2}}$. The optimal distribution is uniform over the domain in\nCartesian coordinates.based on Shannon\u0027s 12th theorem, we show that in the case\nof a single qubit the number of distinguishable states is\n$W(\\alpha_1,\\alpha_2,n)=|\\alpha_1-\\alpha_2|\\sqrt{\\frac{2n}{\\pi e}}$, where\n$(\\alpha_1,\\alpha_2)$ is the angle interval from which the states are chosen.\nIn the general case of an $N$-dimensional Hilbert space and an area $\\Omega$ of\nthe domain on the unit sphere from which the states are chosen, the number of\ndistinguishable states is $W(N,n,\\Omega)=\\Omega(\\frac{2n}{\\pi\ne})^{\\frac{N-1}{2}}$. The optimal distribution is uniform over the domain in\nCartesian coordinates.",
"arxiv_id": "quant-ph/0112075",
"authors": [
"Lev B. Levitin",
"Tommaso Toffoli",
"Zac D. Walton"
],
"categories": [
"quant-ph"
],
"title": "Information and Distinguishability of Ensembles of Identical Quantum States",
"url": "https://arxiv.org/abs/quant-ph/0112075"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "7436b0fc-3395-46c9-b0a3-5b402ae4e5c4",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}