Quantum Random Access Codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.
@article{arxiv.1905.06726,
title = {Sequential random access codes and self-testing of quantum measurement instruments},
author = {Karthik Mohan and Armin Tavakoli and Nicolas Brunner},
journal= {arXiv preprint arXiv:1905.06726},
year = {2019}
}