Understand
One of the great challenges of quantum foundations and quantum information theory is the characterisation of the relationship between entanglement and the violation of Bell inequalities.
- It is well known that in specific scenarios these two can behave differently, from local hidden-variable models for entangled quantum states in restricted Bell scenarios, to maximal violations of Bell inequalities not concurring with maximal entanglement.
- In this paper we put forward a simple proof that there exist quantum states, whose entanglement content, as measured by the Schmidt number, cannot be device-independently certified for all possible sequential measurements on any number of copies.
- While the bigger question: \textit{can the presence of entanglement always be device-independently certified?} remains open, we provide proof that quantifying entanglement device-independently is not always possible, even beyond the standard Bell scenario.