Quantum Test for Higher Order Gowers Norms
R.W.S. Westdorp (TU Delft - Electrical Engineering, Mathematics and Computer Science)
J Briët – Mentor
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
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.