We present a device-independent protocol to test if a given black-box measurement device is entangled, that is, has entangled eigenstates. Our scheme involves three parties and is inspired by entanglement swapping; the test uses the Clauser-Horne-Shimony-Holt Bell inequality, checked between each pair of parties. In the case where all particles are qubits, we characterize quantitatively the deviation of the measurement device from a perfect Bell-state measurement.

In this Letter we compute an analogue of Tsirelson's bound for Hardy's test of nonlocality, that is, the maximum violation of locality constraints allowed by the quantum formalism, irrespective of the dimension of the system. The value is found to be the same as the one achievable already with two-qubit systems, and we show that only a very specific class of states can lead to such maximal value, thus highlighting Hardy's test as a device-independent self-test protocol for such states. By considering realistic constraints in Hardy's test, we also compute device-independent upper bounds on this violation and show that these bounds are saturated by two-qubit systems, thus showing that there is no advantage in using higher-dimensional systems in experimental implementations of such test.Introduction.-The development of quantum information science is based on a recurrent pattern: nonclassical features of quantum physics, previously considered as mind-boggling and worth only of philosophical chat, are found to have an operational meaning and even to be potentially useful for applications. One of the discoveries that triggered this development is the prediction and observation of the violation of Bell inequalities [1]. This observation implies that correlations obtained by measuring separated quantum systems locally cannot be simulated classically without communication, a fact that is often referred to as nonlocality.Within quantum information, nonlocality has undergone an interesting parable. For many years, it has been put aside as having fulfilled its role: the loathed local variables models having been disposed of forever, one could peacefully concentrate on entanglement theory. Only few researchers kept on believing that this very intriguing observation could be useful for something in itself. The latter view was vindicated a few years ago, when it was noticed that nonlocality allows device-independent assessments: indeed, nonlocality is assessed only from the input-output statistics of the measurement, without reference to the degree of freedom that is being measured. This powerful type of assessment is sensitive to the existence of undesired sidechannels and will be ideal for certification of future quantum devices. So far, device-independent results are available for the security of quantum cryptography [2,3], the quality of sources [4,5] and measurement devices [6], the amount of randomness that one can generate [7,8]. In this paper, we study the possibility of device-independent assessment of one of the earliest proposals to check nonlocality: it used to be called Hardy's paradox but, in the spirit of quantum informa-

Entanglement allows for the nonlocality of quantum theory, which is the resource behind device-independent quantum information protocols. However, not all entangled quantum states display nonlocality, and a central question is to determine the precise relation between entanglement and nonlocality. Here we present the first general test to decide whether a quantum state is local, and that can be implemented by semidefinite programming. This method can be applied to any given state and for the construction of new examples of states with local hidden-variable models for both projective and general measurements. As applications we provide a lower bound estimate of the fraction of two-qubit local entangled states and present new explicit examples of such states, including those which arise from physical noise models, Bell-diagonal states, and noisy GHZ and W states.Introduction.-Entanglement is one of the defining properties of quantum theory, playing a central role in quantum information science. One of the most astonishing consequences of entanglement is that local measurements on composite quantum systems can produce correlations which are impossible to reproduce by any classical mechanism satisfying natural notions of local causality [1]. Such correlations are the key aspect behind the famous nonlocality of quantum theory, and they are witnessed by the violation of Bell inequalities [2]. Witnessing nonlocality certifies the entanglement of the underlying quantum state in a way which makes no assumptions about the functioning of the apparatuses used, a realisation which led to the development of the field of deviceindependent quantum information.