2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/89907We 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.10 pages, 1 figure, IQSA 2001Quantum Physicstext