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Bell's theorem, and its experimental tests, has shown that the two premises for Bell's inequality - locality and objective reality - cannot both hold in nature, as Bell's inequality is broken. A simple test is proposed, which for the first…

Local realism in recent experiments is excluded on condition of freedom or randomness of choice combined with no signaling between observers by implementations of simple quantum models. Both no-signaling and the underlying quantum model can…

Derivation of the full set of Bell inequalities involving correlation functions, for two parties, with binary observables, and N possible local settings is not as easy as it seemed. The proof of v1 is wrong. Additionaly one can find a…

Understanding the quantitative relation between entanglement and Bell nonlocality is a long-standing open problem of fundamental and practical interest. Here, we tackle this problem in a general Bell scenario. {We observe that lying in the…

One of the most notable aspects of quantum systems is that their components can exhibit correlations much stronger than those allowed by classical physics. Two examples of quantum correlations are quantum entanglement and Bell nonlocality,…

We examine the satisfaction of Bell criteria for single realizations of quantum systems. This is possible via the joint noisy measurement of all observables involved in the Bell test.We readily find that every outcome violates Bell bounds…

We prove a tight and close-to-optimal lower bound on the effectiveness of local quantum measurements (without classical communication) at discriminating any two bipartite quantum states. Our result implies, for example, that any two…

We derive two classes of multi-mode Bell inequalities under local realistic assumptions, which are violated only by the entangled states negative under partial transposition in accordance with the Peres conjecture. Remarkably, the failure…

A 3-setting Bell-type inequality enforced by the indeterminacy relation of complementary local observables is proposed as an experimental test of the 2-qubit entanglement. The proposed inequality has an advantage of being a sufficient and…

The nonlocality of certain quantum states can be revealed by using local filters before performing a standard Bell test. This phenomenon, known as hidden nonlocality, has been so far demonstrated only for a restricted class of measurements,…

Any Bell test consists of a sequence of measurements on a quantum state in space-like separated regions. Thus, a state is better than others for a Bell test when, for the optimal measurements and the same number of trials, the probability…

For the case of two spin-1/2 particles in the singlet state, we provide a GHZ-type proof of Bell's theorem by using the idea of postselected measurements. Furthermore, we show that in spite of the low efficiency of the detectors one can…

A quantum state can be characterized from the violation of a Bell inequality. The well-known CHSH inequality for example can be used to quantify the fidelity (up to local isometries) of the measured state with respect to the singlet state.…

We improve the test to show the impossibility of a quantum theory based on real numbers by a larger ratio of complex-to-real bound on a Bell-type parameter. In contrast to previous theoretical and experimental proposals the test requires…

With Bell's inequalities one has a formal expression to show how essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a simple experimental arrangement. For the case of…

There are bipartite quantum nonlocal correlations requiring very low detection efficiency to reach the loophole-free regime but that need too many measurement settings to be practical for actual experiments. This leads to the general…

We introduce an all-versus-nothing proof of impossibility of Einstein-Podolsky-Rosen's local elements of reality for two photons entangled both in polarization and path degrees of freedom, which leads to a Bell's inequality where the…

Bell inequality tests where the detection efficiency is below a certain threshold $\eta_{\rm{crit}}$ can be simulated with local hidden-variable models. Here, we introduce a method to identify Bell tests requiring low $\eta_{\rm{crit}}$ and…

Bell nonlocality plays a fundamental role in quantum theory. Numerous tests of the Bell inequality have been reported since the ground-breaking discovery of the Bell theorem.Up to now, however, most discussions of the Bell scenario have…

Here, we consider the Bell experiment for a system described by multipartite states in the case where n-dichotomic observables are measured per site. If n is two, we consider a two-setting Bell experiment. If n is three, we consider a…