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Measurements in the quantum domain can exceed classical notions. This concerns fundamental questions about the nature of the measurement process itself, as well as applications, such as their function as building blocks of quantum…

We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on observed data only but…

Quantum nonlocality is a counterintuitive phenomenon that lies beyond the purview of causal influences. Recently, Bell inequalities have been generalized to the case of quantum inputs, leading to a powerful family of semi-quantum Bell…

We study the Bell nonlocality of high dimensional quantum systems based on quantum entanglement. A quantitative relationship between the maximal expectation value B of Bell operators and the quantum entanglement concurrence C is obtained…

Quantum entanglement plays a central role in many areas of physics, from quantum information science to many-body systems. In order to grasp the essence of this phenomenon, it is fundamental to understand how different manifestations of…

While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure-state entanglement and nonlocality is poorly understood. In fact,…

A well-known manifestation of quantum entanglement is that it may lead to correlations that are inexplicable within the framework of a locally causal theory --- a fact that is demonstrated by the quantum violation of Bell inequalities. The…

We study local-realistic inequalities, Bell-type inequalities, for bipartite pure states of finite dimensional quantum systems -- qudits. There are a number of proposed Bell-type inequalities for such systems. Our interest is in relating…

Techniques developed for device-independent characterizations allow one to certify certain physical properties of quantum systems without assuming any knowledge of their internal workings. Such a certification, however, often relies on the…

A set of Bell inequalities classifying the quantum entanglement of four-qubit states is presented. These inequalities involve only two measurement settings per observer and can characterize fully separable, bi-separable and tri-separable…

We study the relation between violation of Bell inequalities and distillability properties of quantum states. Recently, D\"ur has shown that there are some multiparticle bound entangled states, non-separable and non-distillable, that…

Nonlocality, manifested by the violation of Bell inequalities, indicates entanglement within a joint quantum system. A natural question is how much entanglement is required for a given nonlocal behavior. Here, we explore this question by…

There is no doubt about the fact that entanglement and nonlocality are distinct resources. It is acknowledged that a clear illustration of this point is the difference between maximally entangled states and states that maximally violate a…

Bell nonlocality -- the existence of quantum correlations that cannot be explained by classical means -- is certainly one of the most striking features of quantum mechanics. Its range of applications in device-independent protocols is…

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…

It is an established fact that entanglement is a resource. Sharing an entangled state leads to non-local correlations and to violations of Bell inequalities. Such non-local correlations illustrate the advantage of quantum resources over…

Quantum information science has profoundly changed the ways we understand, store, and process information. A major challenge in this field is to look for an efficient means for classifying quantum state. For instance, one may want to…

From the consideration of measuring bipartite mixed states by separable pure states, we introduce algebraic sets in complex projective spaces for bipartite mixed states as the degenerating locus of the measurement. These algebraic sets are…

In Bell scenario, any nonlocal correlation, shared between two spatially separated parties, can be modeled deterministically either by allowing communications between the two parties or by restricting their free will in choosing the…

We present new bell inequalities for arbitrary dimensional bipartite quantum systems. The maximal violation of the inequalities is computed. The Bell inequality is capable of detecting quantum entanglement of both pure and mixed quantum…