Robust certification of unsharp instruments through sequential quantum advantages in a prepare-measure communication game

TL;DR

This paper introduces a prepare-measure communication game demonstrating quantum advantage over classical theories, enabling semi-device-independent certification of quantum states and measurements, and explores sequential sharing of quantum contextuality with robustness to noise.

Contribution

It proposes a new communication game that certifies quantum states and measurements, and analyzes sequential sharing of quantum advantage with noise robustness.

Findings

Quantum theory outperforms classical non-contextual models in the game.

Optimal success probability certifies unsharp measurement parameters.

Robust scheme demonstrates certification despite noise.

Abstract

Communication games are one of the widely used tools that are designed to demonstrate quantum supremacy over classical resources. In that, two or more parties collaborate to perform an information processing task to achieve the highest success probability of winning the game. We propose a specific two-party communication game in the prepare-measure scenario that relies on an encoding-decoding task of specific information. We first demonstrate that quantum theory outperforms the classical preparation non-contextual theory, and the optimal quantum success probability of such a communication game enables the semi-device-independent certification of qubit states and measurements. Further, we consider the sequential sharing of quantum preparation contextuality and show that, at most, two sequential observers can share the quantum advantage. The sub-optimal quantum advantages for two sequential observers form an optimal pair that certifies a unique value of the unsharpness parameter of the first observer. Since the practical implementation inevitably introduces noise, we devised a scheme to demonstrate the robust certification of the states and unsharp measurement instruments of both the sequential observers.