Information and Distinguishability of Ensembles of Identical Quantum States

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dc.creatorLevitin, Lev B.
dc.creatorToffoli, Tommaso
dc.creatorWalton, Zac D.
dc.date2001-12-12
dc.date.accessioned2026-07-07T06:03:21Z
dc.date.available2026-07-07T06:03:21Z
dc.descriptionWe 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 $W(α_1,α_2,n)=|α_1-α_2|\sqrt{\frac{2n}{πe}}$, where $(α_1,α_2)$ is the angle interval from which the states are chosen. In the general case of an $N$-dimensional Hilbert space and an area $Ω$ of the domain on the unit sphere from which the states are chosen, the number of distinguishable states is $W(N,n,Ω)=Ω(\frac{2n}{πe})^{\frac{N-1}{2}}$. 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 $W(α_1,α_2,n)=|α_1-α_2|\sqrt{\frac{2n}{πe}}$, where $(α_1,α_2)$ is the angle interval from which the states are chosen. In the general case of an $N$-dimensional Hilbert space and an area $Ω$ of the domain on the unit sphere from which the states are chosen, the number of distinguishable states is $W(N,n,Ω)=Ω(\frac{2n}{πe})^{\frac{N-1}{2}}$. The optimal distribution is uniform over the domain in Cartesian coordinates.
dc.description10 pages, 1 figure, IQSA 2001
dc.identifierhttps://arxiv.org/abs/quant-ph/0112075
dc.identifierhttp://arxiv.org/abs/quant-ph/0112075
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/89907
dc.subjectQuantum Physics
dc.titleInformation and Distinguishability of Ensembles of Identical Quantum States
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