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One of the great challenges of quantum foundations and quantum informationtheory is the characterisation of the relationship between entanglement and theviolation of Bell inequalities. It is well known that in specific scenariosthese two can behave differently, from local hidden-variable models forentangled quantum states in restricted Bell scenarios, to maximal violations ofBell inequalities not concurring with maximal entanglement. In this paper weput forward a simple proof that there exist quantum states, whose entanglementcontent, as measured by the Schmidt number, cannot be device-independentlycertified for all possible sequential measurements on any number of copies.While the bigger question: \textit{can the presence of entanglement always bedevice-independently certified?} remains open, we provide proof thatquantifying entanglement device-independently is not always possible, evenbeyond the standard Bell scenario.

The Schmidt number of a quantum state cannot always be device-independently certified