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Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)
Quantum t-designs: t-wise Independence in the Quantum World
San Diego, California
June 13-March 16
ISBN: 0-7695-2780-9
Andris Ambainis, University of Waterloo, Canada
Joseph Emerson, University of Waterloo, Canada
A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate quantum t-designs for arbitrary t. We then show that an approximate 4-design provides a derandomization of the statedistinction problem considered by Sen (quant-ph/0512085), which is relevant to solving certain instances of the hidden subgroup problem.
Citation:
Andris Ambainis, Joseph Emerson, "Quantum t-designs: t-wise Independence in the Quantum World," ccc, pp.129-140, Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07), 2007
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