A proof of Bell's theorem without inequalities 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 theorem based on an entangled state of 2n qubits (with n odd) shared between two distant observers. A generalized CHSH inequality is formulated for 2n qubits and it is shown that quantum mec...

We study the consequences of ‘super-quantum non-local correlations’ as represented by the PR-box model of Popescu and Röhrlich, and show PR-boxes can enhance the capacity of noisy interference channels between two senders and two receivers. PR-box correlations violate Bell/CHSH inequalities and are thus stronger – more non-local – than quantum mechanics; yet weak enough to respect special relat...

We perform analysis of Bell's arguments (and their generalizations) on the basis of the frequency approach to probability theory (R. von Mises, 1919). This analysis demonstrated that there are no physical arguments which support the existence of 'probability dis-tributions' which were formally used in all investigations based on the conventional (Kolmogorov, 1933) approach to probability theory...

This thesis describes the development of a free-space quantum key distribution system which has the ability to provide unconditionally secure communication between two parties: Alice and Bob. The system exploits the quantum mechanical property of entanglement in order to generate a key. Security is then guaranteed by the No-Cloning theorem and the laws of quantum mechanics which prevent a quant...

Entanglement in quantum mechanics contradicts local realism and is a manifestation of quantum nonlocality. Its presence can be detected through the violation of Bell, or Clauser-Horne-Shimony-Holt (CHSH) inequalities. Paradigmatic quantum systems provide examples of both, nonentangled and entangled states. Here, we consider a minimal complexity setup consisting of six Majorana zero modes. We fi...

For the purpose of the nonlocality test, we propose a general correlation observable of two parties by utilizing local d-outcome measurements with SU(d) transformations and classical communications. Generic symmetries of the SU(d) transformations and correlation observables are found for the test of nonlocality. It is shown that these symmetries dramatically reduce the number of numerical varia...

We investigate the complexity cost of demonstrating the key types of nonclassical correlations — Bell inequality violation, EPR-steering, and entanglement — with independent agents, theoretically and in a photonic experiment. We show that the complexity cost exhibits a hierarchy among these three tasks, mirroring the recently-discovered hierarchy for how robust they are to noise. For Bell inequ...

Proving security of device-independent (DI) cryptographic protocols has been regarded to be a complex and tedious task. In this work we show that a newly developed tool, the “entropy accumulation theorem” of Dupuis et al. [DFR16], can be effectively applied to give fully general proofs of DI security. At a high level our technique amounts to establishing a reduction to the scenario in which the...

We consider tripartite entangled states for continuous variable systems of EPR type, which generalise the famous bipartite CV EPR states (eigenvectors of conjugate choices X1−X2, P1+ P2, of the systems’ relative position and total momentum variables). We give the regularised forms of such tripartite EPR states in second-quantised formulation, and derive their Wigner functions. This is directly ...

Bell proved in 1965 [ 1 ] that nonlocality is an unavoidable property of quantum theory. By assuming locality, he derived a set of inequalities which, he then showed. are violated by the predictions of quantum theory. Since then a number of different Bell inequalities have been discovered, the most important of these are the Clauser, Horne, Shimony, and Holt (CHSH ) inequalities [ 21 derived in...