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Quantum Random Access Codes (QRACs) are key tools for a variety of protocolsin quantum information theory. These are commonly studied inprepare-and-measure scenarios in which a sender prepares states and a receivermeasures them. Here, we consider a three-party prepare-transform-measurescenario in which the simplest QRAC is implemented twice in sequence based onthe same physical system. We derive optimal trade-off relations between the twoQRACs. We apply our results to construct semi-device independent self-tests ofquantum instruments, i.e. measurement channels with both a classical andquantum output. Finally, we show how sequential QRACs enable inference of upperand lower bounds on the sharpness parameter of a quantum instrument.

Sequential random access codes and self-testing of quantum measurement instruments