Quantum Test for Higher Order Gowers Norms

Student report (2021)

Authors

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

Contributors

J Briët (supervisor 1)
Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright: © 2021 Rik Westdorp
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Published Date

26-02-2021

Language

English

Reuse Rights

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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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