TY - JOUR

T1 - Estimating the spectrum of a density operator

AU - Keyl, M.

AU - Werner, R. F.

PY - 2001

Y1 - 2001

N2 - Given N quantum systems prepared according to the same density operator rho. we propose a measurement on the N-fold system that approximately yields the spectrum of rho. 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 rho in decreasing order. We show convergence of these estimates in the limit N and that the probability for errors decreases exponentially with a rate we compute explicitly.

AB - Given N quantum systems prepared according to the same density operator rho. we propose a measurement on the N-fold system that approximately yields the spectrum of rho. 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 rho in decreasing order. We show convergence of these estimates in the limit N and that the probability for errors decreases exponentially with a rate we compute explicitly.

U2 - 10.1103/PhysRevA.64.052311

DO - 10.1103/PhysRevA.64.052311

M3 - Article

VL - 64

SP - 052311

JO - Phys. Rev. A

JF - Phys. Rev. A

SN - 2469-9934

IS - 5

ER -