  Quantum mechanics provides means of generating genuine randomness that is
impossible with deterministic classical processes. Remarkably, the
unpredictability of randomness can be certified in a self-testing manner that
is independent of implementation devices. Here, we present an experimental
demonstration of self-testing quantum random number generation based on an
detection-loophole free Bell test with entangled photons. In the randomness
analysis, without the assumption of independent identical distribution, we
consider the worst case scenario that the adversary launches the most powerful
attacks against quantum adversary. After considering statistical fluctuations
and applying an 80 Gb $\times$ 45.6 Mb Toeplitz matrix hashing, we achieve a
final random bit rate of 114 bits/s, with a failure probability less than
$10^{-5}$. Such self-testing random number generators mark a critical step
towards realistic applications in cryptography and fundamental physics tests.
