# Experimental comparison of tomography and self-testing in certifying entanglement

## TL;DR

This paper compares tomography and self-testing methods for certifying entanglement in two-qubit states, demonstrating that self-testing provides nearly as accurate fidelity estimates as full tomography even with open detection loopholes.

## Contribution

It introduces a robust data analysis approach for self-testing that accounts for finite sample fluctuations and compares its effectiveness to standard tomography.

## Key findings

- Self-testing fidelity is approximately 98.8% of tomography fidelity.
- Self-testing performs well even with open detection and locality loopholes.
- The method is robust against finite sample fluctuations.

## Abstract

We assess the quality of a source of allegedly pure two-qubit states using both standard tomography and methods inspired by device-independent self-testing. Even when the detection and locality loopholes are open, the latter methods can dispense with modelling of the system and the measurements. However, due to finite sample fluctuations, the estimated probability distribution usually does not satisfy the no-signaling conditions exactly. We implement data analysis that is robust against these fluctuations. We demonstrate a high ratio $f_s/f_t\approx 0.988$ between the fidelity estimated from self-testing and that estimated from full tomography, proving high performance of self-testing methods.