  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.
