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Large Deviation Bounds for kdesigns
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"... We present a technique for derandomising large deviation bounds of functions on the unitary group. We replace the Haar distribution with a pseudorandom distribution, a kdesign. kdesigns have the first k moments equal to those of the Haar distribution. The advantage of this is that (approximate) k ..."
Abstract

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We present a technique for derandomising large deviation bounds of functions on the unitary group. We replace the Haar distribution with a pseudorandom distribution, a kdesign. kdesigns have the first k moments equal to those of the Haar distribution. The advantage of this is that (approximate) kdesigns can be implemented efficiently, whereas Haar random unitaries cannot. We find large deviation bounds for unitaries chosen from a kdesign and then illustrate this general technique with three applications. We first show that the von Neumann entropy of a pseudorandom state is almost maximal. Then we show that, if the dynamics of the universe produces a kdesign, then suitably sized subsystems will be in the canonical state, as predicted by statistical mechanics. Finally we show that pseudorandom states are useless for measurement based quantum computation. 1
Variations on classical and quantum extractors
 In Information Theory (ISIT), 2014 IEEE International Symposium on
, 2014
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