Phys. Rev. A 64, 052311 (2001) [5 pages]Estimating the spectrum of a density operatorReceived 7 March 2001; published 15 October 2001 Given N quantum systems prepared according to the same density operator ρ, we propose a measurement on the N-fold system that 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 ρ in decreasing order. We show convergence of these estimates in the limit N⃗∞, and that the probability for errors decreases exponentially with a rate we compute explicitly. © 2001 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.64.052311
DOI:
10.1103/PhysRevA.64.052311
PACS:
03.67.Lx, 03.65.Ca
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