Generalizations of Boxworld

Boxworld is a toy theory that can generate extremal nonlocal correlations known as PR boxes. These have been well established as an important tool to examine general nonlocal correlations, even beyond the correlations that are possible in quantum theory. We modify boxworld to include new features. The first modification affects the construction of joint systems such that the new theory allows entangled measurements as well as entangled states in contrast to the standard version of boxworld. The extension to multipartite systems and the consequences for entanglement swapping are analysed. Another modification provides continuous transitions between classical probability theory and boxworld, including the algebraic expression for the maximal CHSH violation as a function of the transition parameters.Comment: In Proceedings QPL 2011, arXiv:1210.029

Quantum Correlations and Quantum Non-Locality: A Review and a Few New Ideas

In this paper we make an extensive description of quantum non-locality, one of the most intriguing and fascinating facets of quantum mechanics. After a general presentation of several studies on this subject, we consider if quantum non-locality, and the friction it carries with special relativity, can eventually find a "solution" by considering higher dimensional spaces.Comment: 1

The non-locality of n noisy Popescu-Rohrlich boxes

We quantify the amount of non-locality contained in n noisy versions of so-called Popescu-Rohrlich boxes (PRBs), i.e., bipartite systems violating the CHSH Bell inequality maximally. Following the approach by Elitzur, Popescu, and Rohrlich, we measure the amount of non-locality of a system by representing it as a convex combination of a local behaviour, with maximal possible weight, and a non-signalling system. We show that the local part of n systems, each of which approximates a PRB with probability $1-\epsilon$, is of order $\Theta(\epsilon^{\lceil n/2\rceil})$ in the isotropic, and equal to $(3\epsilon)^n$ in the maximally biased case.Comment: 14 pages, v2: published versio

Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality

Characterizing quantum correlations in terms of information-theoretic principles is a popular chapter of quantum foundations. Traditionally, the principles adopted for this scope have been expressed in terms of conditional probability distributions, specifying the probability that a black box produces a certain output upon receiving a certain input. This framework is known as "device-independent". Another major chapter of quantum foundations is the information-theoretic characterization of quantum theory, with its sets of states and measurements, and with its allowed dynamics. The different frameworks adopted for this scope are known under the umbrella term "general probabilistic theories". With only a few exceptions, the two programmes on characterizing quantum correlations and characterizing quantum theory have so far proceeded on separate tracks, each one developing its own methods and its own agenda. This paper aims at bridging the gap, by comparing the two frameworks and illustrating how the two programmes can benefit each other.Comment: 61 pages, no figures, published versio

Non-locality and Communication Complexity

Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the information counterpart of computing. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used to obtain dramatic advantages for such tasks. We review the area of quantum communication complexity, and show how it connects the foundational physics questions regarding non-locality with those of communication complexity studied in theoretical computer science. The first examples exhibiting the advantage of the use of qubits in distributed information-processing tasks were based on non-locality tests. However, by now the field has produced strong and interesting quantum protocols and algorithms of its own that demonstrate that entanglement, although it cannot be used to replace communication, can be used to reduce the communication exponentially. In turn, these new advances yield a new outlook on the foundations of physics, and could even yield new proposals for experiments that test the foundations of physics.Comment: Survey paper, 63 pages LaTeX. A reformatted version will appear in Reviews of Modern Physic