Phys. Rev. Lett. 97, 170502 (2006) [4 pages]Efficient Quantum Circuits for Schur and Clebsch-Gordan TransformsReceived 13 July 2004; revised 3 March 2006; published 27 October 2006 The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient {size poly[n,d,log(1/ϵ)] for accuracy ϵ} quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. Our circuits provide explicit efficient methods for solving such diverse problems as estimating the spectrum of a density operator, quantum hypothesis testing, and communicating without a shared reference frame. We thus render tractable a large series of methods for extracting resources from quantum systems and for numerous quantum information protocols. © 2006 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.97.170502
DOI:
10.1103/PhysRevLett.97.170502
PACS:
03.67.Lx, 03.67.Mn
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