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Symmetric functions of qubits in an unknown basis

2009
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Physical Review A. Atomic, Molecular, and Optical Physics
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Consider an n qubit computational basis state corresponding to a bit string x, which has had an unknown local unitary applied to each qubit, and whose qubits have been reordered by an unknown permutation. We show that, given such a state with Hamming weight |x| at most n/2, it is possible to reconstruct |x| with success probability 1 - |x|/(n-|x|+1), and thus to compute any symmetric function of x. We give explicit algorithms for computing whether or not |x| is at least t for some t, and for

doi:10.1103/physreva.79.062316
fatcat:vwk2pbi7kndbreudvvie7hsuzq