Quantum Test for Higher Order Gowers Norms

Student report (2021)

Authors

R.W.S. Westdorp Electrical Engineering, Mathematics and Computer Science

Contributors

Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2021 Rik Westdorp
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Published Date

26-02-2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In this work, a quantum self-test which certifies that measurements of a quantum device have a large Gowers norm of order k is presented and analysed. The test protocol is described as a two-player quantum game, in which players provide answers based on measurements on subsystems of a maximally entangled
bipartite state. The protocol makes use of 2k +1 subtests. It is shown that strategies that succeed in the test with success rate 1-E must have a Gowers norm larger than 1-O(E). This test generalizes measurement tests that certify measurements based on the second order Gowers norm.

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