密度算子的谱估计
Estimating the spectrum of a density operator
摘要：
给定按相同密度算符ρ制备的N个量子系统，我们提出了对N重系统的一种测量，它近似地产生了ρ的谱.所提出的观测量的投影根据N个点上排列的不可约表示分解希尔伯特空间，并标记为Young标架，其相对行长度按降序估计ρ的特征值。我们证明了这些估计在极限N \to \infty中的收敛性，并且错误的概率随着我们明确计算的速率呈指数下降。
英文摘要：
Given N quantum systems prepared according to the same density operator ρ, we propose a measurement on the N-fold system which approximately yields the spectrum of ρ. The projections of the proposed observable decompose the Hilbert space according to the irreducible representations of the permutations on N points, and are labeled by Young frames, whose relative row lengths estimate the eigenvalues of ρin decreasing order. We show convergence of these estimates in the limit N\to\infty, and that the probability for errors decreases exponentially with a rate we compute explicitly.
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