arXiv quant-ph/01120752001-12-12quant-ph

全同量子态系综的信息与可分辨性

Information and Distinguishability of Ensembles of Identical Quantum States

Lev B. Levitin, Tommaso Toffoli, Zac D. Walton

备注：: 10 pages, 1 figure, IQSA 2001

摘要：

我们考虑一个固定的量子测量$n$相同的副本的量子态。利用严格的量子可测性概念，我们考虑了在$n$上进行的固定量子测量，该测量是量子态的相同副本。使用基于香农第12定理的严格的可分辨性概念，我们证明了在单个量子比特的情况下，可分辨状态的数量是$W(α_1,α_2,n)=|α_1-α_2|\sqrt{\frac{2n}{πe}}$，其中$(α_1,α_2)$是从其中选择状态的角度间隔。在一个$N$维希尔伯特空间和一个区域$Ω$的单位球面上的状态选择域的一般情况下，可区分状态的数量是$W(N,n,Ω)=Ω(\frac{2n}{πe})^{\frac{N-1}{2}}$。基于Shannon第12定理，我们证明了在单量子比特的情况下，可区分态的个数为$W(α_1,α_2,n)=|α_1-α_2|\sqrt{\frac{2n}{πe}}$，其中$(α_1,α_2)$是选择态的角度区间.在一个$N$维希尔伯特空间和一个区域$Ω$的单位球面上的状态选择域的一般情况下，可区分状态的数量是$W(N,n,Ω)=Ω(\frac{2n}{πe})^{\frac{N-1}{2}}$。最优分布在笛卡尔坐标系中的域上是均匀的。

英文摘要：

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 $W(α_1,α_2,n)=|α_1-α_2|\sqrt{\frac{2n}{πe}}$, 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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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