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

## TL;DR

This paper explores sequential quantum random access codes (QRACs) in a three-party scenario, deriving optimal trade-offs, enabling self-testing of quantum instruments, and bounding their sharpness parameter.

## Contribution

It introduces a framework for sequential QRACs, deriving trade-offs and applying them to semi-device independent self-testing and parameter bounds of quantum instruments.

## Key findings

- Derived optimal trade-off relations for sequential QRACs.
- Constructed semi-device independent self-tests for quantum measurement channels.
- Established bounds on the sharpness parameter of quantum instruments.

## Abstract

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.