Noise-tolerant testing of high entanglement of formation

TL;DR

This paper introduces noise-tolerant tests for certifying high-dimensional entanglement in quantum devices, applicable in realistic noisy conditions, and provides bounds on the entanglement cost for quantum advantage in non-local games.

Contribution

It constructs a family of noise-tolerant non-local games that certify high entanglement, extending the applicability of entanglement certification in noisy experimental settings.

Findings

Family of non-local games certifies entanglement of formation $\Omega(n)$

Tests are robust to noise without fault-tolerant technology

Provides lower bounds on entanglement cost for quantum advantage

Abstract

In this work we construct tests that allow a classical user to certify high dimensional entanglement in uncharacterized and possibly noisy quantum devices. We present a family of non-local games $\{G_n\}$ that for all $n$ certify states with entanglement of formation $\Omega(n)$. These tests can be derived from any bipartite non-local game with a classical-quantum gap. Furthermore, our tests are noise-tolerant in the sense that fault tolerant technologies are not needed to play the games; entanglement distributed over noisy channels can pass with high probability, making our tests relevant for realistic experimental settings. This is in contrast to, e.g., results on self-testing of high dimensional entanglement, which are only relevant when the noise rate goes to zero with the system's size $n$. As a corollary of our result, we supply a lower-bound on the entanglement cost of any state achieving a quantum advantage in a bipartite non-local game. Our proof techniques heavily rely on ideas from the work on classical and quantum parallel repetition theorems.