Quantum t-designs: t-wise independence in the quantum world

Andris Ambainis; Joseph Emerson

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Quantum t-designs: t-wise independence in the quantum world

Andris Ambainis·Joseph Emerson

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Abstract

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 state-distinction problem considered by Sen (quant-ph/0512085), which is relevant to solving certain instances of the hidden subgroup problem.

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Andris Ambainis, Joseph Emerson. 2007-02-06. Quantum t-designs: t-wise independence in the quantum world. https://arxiv.org/abs/quant-ph/0701126

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