Practical parallel self-testing of Bell states via magic rectangles

TL;DR

This paper presents a practical method for self-testing multiple Bell states in parallel using magic rectangle games, requiring minimal quantum capabilities and demonstrating robustness suitable for quantum verification tasks.

Contribution

It introduces a new self-testing protocol for multiple Bell states using $3 imes n$ magic rectangle games with minimal measurement requirements and robustness analysis.

Findings

Self-test for $n$ Bell states with single-qubit measurements.

Protocol has small input sizes and is robust to noise.

Introduces a one-side-local winning strategy for the magic square game.

Abstract

Self-testing is a method to verify that one has a particular quantum state from purely classical statistics. For practical applications, such as device-independent delegated verifiable quantum computation, it is crucial that one self-tests multiple Bell states in parallel while keeping the quantum capabilities required of one side to a minimum. In this work, we use the $3 \times n$ magic rectangle games (generalizations of the magic square game) to obtain a self-test for $n$ Bell states where the one side needs only to measure single-qubit Pauli observables. The protocol requires small input sizes [constant for Alice and $O(\log n)$ bits for Bob] and is robust with robustness $O(n^{5/2} \sqrt{\varepsilon})$, where $\varepsilon$ is the closeness of the ideal (perfect) correlations to those observed. To achieve the desired self-test, we introduce a one-side-local quantum strategy for the magic square game that wins with certainty, we generalize this strategy to the family of $3 \times n$ magic rectangle games, and we supplement these nonlocal games with extra check rounds (of single and pairs of observables).