Tolerant testing of stabilizer states with a polynomial gap via a generalized uncertainty relation

TL;DR

This paper proves a conjecture about tolerant stabilizer testing, introducing a generalized uncertainty relation for Pauli operators that significantly improves testing parameters.

Contribution

It establishes a tolerant stabilizer testing algorithm with exponential parameter improvements using a novel generalized uncertainty relation.

Findings

Proves the conjecture of Arunachalam & Dutt on stabilizer testing.

Develops a generalized uncertainty relation for Pauli operators.

Achieves exponential improvements in testing parameters.

Abstract

We prove a conjecture of Arunachalam & Dutt ([AD24]) on the existence of a tolerant stabilizer testing algorithm, and achieve an exponential improvement in the parameters of the tester. Key to our argument is a generalized uncertainty relation for sets of Pauli operators, based on the Lovasz theta function.