Robust certification of quantum instruments through a sequential communication game

TL;DR

This paper introduces a sequential communication game demonstrating quantum advantage in message decoding, enabling robust, semi-device-independent certification of quantum states and measurements, with improved robustness and scalability to higher dimensions.

Contribution

It presents a new sequential communication game that achieves quantum advantage and allows self-testing of quantum devices in a semi-device-independent manner.

Findings

Quantum advantage in message decoding with restricted communication.

Robust semi-device-independent certification of quantum states and measurements.

Enhanced advantage and scalability in higher-dimensional systems.

Abstract

We propose a communication game in the sequential measurement scenario, involving a sender and two receivers with restricted communication among the latter parties. In the framework of the prepare-transform-measure scenario, we find a prominent quantum advantage in the receiver's decoding of the message originally encoded by the sender. We show that an optimal trade-off between the success probabilities of the two receivers enables self-testing of the sender's state preparation, the first receiver's instruments, and the measurement device of the second receiver in a semi-device-independent way. Our protocol enables a more robust certification of the unsharp measurement parameter of the first receiver compared to an earlier protocol. We further generalize our game to higher-dimensional systems, revealing greater quantum advantage with an increase in dimensions.