Robust Self Testing of the Singlet

TL;DR

This paper develops a robust self-testing framework for EPR pairs and measurement operators, demonstrating that near-optimal quantum correlations imply the presence of an approximate EPR pair and measurements.

Contribution

It introduces a general, error-tolerant self-testing method based solely on experimental probabilities, applicable to EPR pairs and local measurements.

Findings

Approaching the Cirel'son bound indicates an approximate EPR pair presence.

Near-Mayers-Yao correlations imply measurements close to ideal qubit operators.

The framework tolerates experimental errors while certifying quantum states and measurements.

Abstract

In this paper, we introduce a general framework to study the concept of robust self testing which can be used to self test EPR pairs and local measurement operators. The result is based only on probabilities obtained from experiment, with tolerance to experimental errors. In particular, we show that if results of experiment come approach the Cirel'son bound, or approximates the Mayers-Yao type correlation, then the experiment must contain an approximate EPR pair. More specifically, there exist local bases in which the physical state is close to an EPR pair, possibly all encoded in a larger environment or ancilla. Moreover, in theses bases the measurements are close to the qubit operators used to achieve the Cirel'son bound or the Mayers-Yao results.