  The sequential quantum random access code (QRAC) allows two or more decoders
to obtain a desired message with higher success probability than the best
classical bounds by appropriately modulating the measurement sharpness. Here,
we propose an entanglement-assisted sequential QRAC protocol which can enable
device-independent tasks. By relaxing the equal sharpness and mutually unbiased
measurement limits, we widen the sharpness modulation region from a
one-dimensional interval to a two-dimensional triangle. Then, we demonstrate
our scheme experimentally and get more than 27 standard deviations above the
classical bound even when both decoders perform approximately projective
measurements. We use the observed success probability to quantify the
connection among sequential QRAC, measurement sharpness, measurement
biasedness, and measurement incompatibility. Finally, we show that our protocol
can be applied to sequential device-independent randomness expansion and our
measurement strategy can enhance the success probability of decoding the entire
input string. Our results may promote a deeper understanding of the
relationship among quantum correlation, quantum measurement, and quantum
information processing.
