  A random access code (RAC) is a strategy to encode a message into a shorter
one in a way that any bit of the original can still be recovered with
nontrivial probability. Encoding with quantum bits rather than classical ones
can improve this probability, but has an important limitation: due to the
disturbance caused by standard quantum measurements, qubits cannot be used more
than once. However, as recently shown by Mohan, Tavakoli, and Brunner [New J.
Phys. 21 083034, (2019)], weak measurements can alleviate this problem,
allowing two sequential decoders to perform better than with the best classical
RAC. We use single photons to experimentally show that these weak measurements
are feasible and nonclassical success probabilities are achievable by two
decoders. We prove this for different values of the measurement strength and
use our experimental results to put tight bounds on them, certifying the
accuracy of our setting. This proves the feasibility of using sequential
quantum RACs for quantum information tasks such as the self-testing of
untrusted devices.
