The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say a Bell inequality is normalized if its absolute value does not exceed 1 for any classical (i.e. local) distribution. Upper and (almost) tight lower bounds have been given in terms of number of outputs of the distribution, number of inputs, an...

The derivation of Bell inequalities requires an assumption of measurement independence, related to the amount of free will experimenters have in choosing measurement settings. Violation of these inequalities by singlet state correlations, as has been experimentally observed, brings this assumption into question. A simple measure of the degree of measurement independence is defined for correlati...

A certain class of parametric down-conversion Bell type experiments has the following features. In the idealized perfect situation it is in only 50% of cases that each observer receives a photon; in the other 50% of cases one observer receives both photons of a pair while the other observer receives none. The standard approach is to discard the events of the second type. Only the remaining ones...

It is often believed that de Finetti’s coherence principle naturally leads, in the finite case, to the Kolmogorov’s probability theory of random phenomena, which then implies Bell’s inequality. Thus, not only a violation of Bell’s inequality looks paradoxical in the Kolmogorovian framework, but it should violate also de Finetti’s coherence principle. Firstly, we show that this is not the case: ...

Quantum steering, the ability of one party to perform a measurement on their side of an entangled system with different outcomes leading to different sets of states for another part of the entangled system arbitrarily far away, is a purely quantum phenomena with no classical analogue. However, it is closely related (and indeed equivalent for pure states) to entanglement and Bell nonlocality. Th...

We report on the realisation of a new test of Bell inequalities using the superposition of type I parametric down conversion produced in two different non-linear crystals pumped by the same laser, but with different polarisations. We discuss the advantages and the possible developments of this configuration. Many experiments have already been devoted to a test of Bell inequalities [1–5], leadin...

First, I show a protocol to faithfully and deterministically teleport an arbitrary 2-qubit state from Alice to Bob. In this protocol two same Bell states are enough for use. Bob can recover the 2-qubit state by performing appropriate unitary operations conditioned on Alice’s two Bell-state measurement outcomes. Then I generalize the 2-qubit teleportation protocol to a N(N ≥ 3)-qubit teleportati...

Until the 1990’s philosophers took it almost for granted that the common cause principle is at odds with quantum theory. Roughly, they argued that a common cause explanation of correlations between four pairs of events leads inevitably to Bell inequalities, and since Bell inequalities are violated in quantum theory, there cannot be a common cause explanation of quantum correlations. Redei and h...

Bell experiments can be used to generate private random numbers. An ideal Bell experiment would involve measuring a state of two maximally entangled qubits, but in practice any state produced is subject to noise. Here we consider how the techniques presented in [1] and [2], i. e. using an optimized Bell inequality, and taking advantage of the fact that the device provider is not our adversary, ...

A memorial conference for John Bell, open to the public, was held at Rutgers University around 20 years ago. I gave there a short talk on Bell’s views about David Bohm’s “hidden variables” formulation of quantum mechanics, a version of quantum mechanics often called the de Broglie-Bohm theory or Bohmian mechanics. This theory was in fact discovered by Louis de Broglie in 1927. In 1952, it was r...