npj Quantum Information (Oct 2021)

# Self-testing quantum systems of arbitrary local dimension with minimal number of measurements

• Shubhayan Sarkar,
• Debashis Saha,
• Jędrzej Kaniewski,
• Remigiusz Augusiak

DOI
https://doi.org/10.1038/s41534-021-00490-3
Journal volume & issue
Vol. 7, no. 1
pp. 1 – 5

## Abstract

Abstract Bell nonlocality as a resource for device-independent certification schemes has been studied extensively in recent years. The strongest form of device-independent certification is referred to as self-testing, which given a device, certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit–qudit entangled states based on violation of a single d-outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, $${{{\mathrm{log}}}\,}_{2}d$$ log 2 d perfect random bits, while it requires only one random bit to encode the measurement choice.