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The violation of Bell's inequality requires a well-designed experiment to validate the result. In experiments using energy-time and time-bin entanglement, initially proposed by Franson in 1989, there is an intrinsic loophole due to the high…

I derive separability inequalities for Bell correlations of observables in arbitrary pure or mixed $N$ Qudit states in $D^N$-dimensional state space. I find states (a continuum of states if $D>3$) including maximally entangled states which…

For more than 80 years, the counterintuitive predictions of quantum theory have stimulated debate about the nature of reality. In his seminal work, John Bell proved that no theory of nature that obeys locality and realism can reproduce all…

A proof of Bell's theorem without inequalities valid for both inequivalent classes of three-qubit entangled states under local operations assisted by classical communication, namely Greenberger-Horne-Zeilinger (GHZ) and W, is described.…

Quantum correlations resulting in violations of Bell inequalities have generated a lot of interest in quantum information science and fundamental physics. In this paper, we address some questions that become relevant in Bell-type tests…

This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…

Quantum entanglement and Bell nonlocality are two phenomena that occur only in quantum systems. In both cases, these are correlations between two subsystems that are classically absent. Traditionally, these phenomena have been measured in…

Bell type inequalities are used to test local realism against quantum theory.In this paper, we consider a two party system with two settings and two possible outcomes on each side, and derive equalities in local theories which are violated…

In this paper we extend the ladder proof of nonlocality without inequalities for two spin-half particles given by Boschi et al [PRL 79, 2755 (1997)] to the case in which the measurement settings of the apparatus measuring one of the…

Nonlocality is the most characteristic feature of quantum mechanics. John Bell, in his seminal 1964 work, proved that local-realism imposes a bound on the correlations among the measurement statistics of distant observers. Surpassing this…

The Bell theorem stands as an insuperable roadblock in the path to a very desired intuitive solution of the EPR paradox and, hence, it lies at the core of the current lack of a clear interpretation of the quantum formalism. The theorem…

Bell's theorem, stating that quantum predictions are incompatible with a local hidden variable description, is a cornerstone of quantum theory and at the center of many quantum information processing protocols. Over the years, different…

Hardy's non-locality theorem for multiple two-level systems is explored in the context of generalized nonlocal theory. We find nonlocal but non-signaling probabilities, providing Hardy's nonlocal argument, which are higher than those in…

According to Bell's theorem, local realism is incompatible with quantum theory. However, it depends on an implied assumption about quantum measurement. We suggest that the assumption might be removed by a detailed quantum analysis of the…

Bell nonlocality between distant quantum systems---i.e., joint correlations which violate a Bell inequality---can be verified without trusting the measurement devices used, nor those performing the measurements. This leads to…

A proof of Bell's theorem without inequalities and involving only two observers is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's…

We explore the link between two concepts: the level of violation of a Bell inequality by a quantum state and discrimination between two states by means of restricted classes of operations, such as local operations and classical…

We propose a entanglement measure for pure $M \otimes N$ bipartite quantum states. We obtain the measure by generalizing the equivalent measure for a $2 \otimes 2$ system, via a $2 \otimes 3$ system, to the general bipartite case. The…

Besides well-known conditions of locality or factorisability, deriving the Bell inequalities requires assuming that the distribution of hidden variables and Alice's and Bob's measurement settings be independent of each other. We show that…

Efficient verification of quantum states and gates is crucial to the development of quantum technologies. Although the sample complexities of quantum state verification and quantum gate verification have been studied by many researchers,…