No nonlocal box is universal

We show that standard nonlocal boxes, also known as Popescu-Rohrlich machines, are not sufficient to simulate any nonlocal correlations that do not allow signalling. This was known in the multipartite scenario, but we extend the result to the bipartite case. We then generalize this result further by showing that no finite set containing any finite-output-alphabet nonlocal boxes can be a universal set for nonlocality.Comment: Additions to the acknowledgements sectio

On the power of non-local boxes

A non-local box is a virtual device that has the following property: given that Alice inputs a bit at her end of the device and that Bob does likewise, it produces two bits, one at Alice's end and one at Bob's end, such that the XOR of the outputs is equal to the AND of the inputs. This box, inspired from the CHSH inequality, was first proposed by Popescu and Rohrlich to examine the question: given that a maximally entangled pair of qubits is non-local, why is it not maximally non-local? We believe that understanding the power of this box will yield insight into the non-locality of quantum mechanics. It was shown recently by Cerf, Gisin, Massar and Popescu, that this imaginary device is able to simulate correlations from any measurement on a singlet state. Here, we show that the non-local box can in fact do much more: through the simulation of the magic square pseudo-telepathy game and the Mermin-GHZ pseudo-telepathy game, we show that the non-local box can simulate quantum correlations that no entangled pair of qubits can in a bipartite scenario and even in a multi-party scenario. Finally we show that a single non-local box cannot simulate all quantum correlations and propose a generalization for a multi-party non-local box. In particular, we show quantum correlations whose simulation requires an exponential amount of non-local boxes, in the number of maximally entangled qubit pairs.Comment: 14 pages, 1 figur

A limit on nonlocality in any world in which communication complexity is not trivial

Bell proved that quantum entanglement enables two space-like separated parties to exhibit classically impossible correlations. Even though these correlations are stronger than anything classically achievable, they cannot be harnessed to make instantaneous (faster than light) communication possible. Yet, Popescu and Rohrlich have shown that even stronger correlations can be defined, under which instantaneous communication remains impossible. This raises the question: Why are the correlations achievable by quantum mechanics not maximal among those that preserve causality? We give a partial answer to this question by showing that slightly stronger correlations would result in a world in which communication complexity becomes trivial.Comment: 13 pages, no figure

On the logical structure of Bell theorems without inequalities

Bell theorems show how to experimentally falsify local realism. Conclusive falsification is highly desirable as it would provide support for the most profoundly counterintuitive feature of quantum theory - nonlocality. Despite the preponderance of evidence for quantum mechanics, practical limits on detector efficiency and the difficulty of coordinating space-like separated measurements have provided loopholes for a classical worldview; these loopholes have never been simultaneously closed. A number of new experiments have recently been proposed to close both loopholes at once. We show some of these novel designs fail in the most basic way, by not ruling out local hidden variable models, and we provide an explicit classical model to demonstrate this. They share a common flaw, which reveals a basic misunderstanding of how nonlocality proofs work. Given the time and resources now being devoted to such experiments, theoretical clarity is essential. Our explanation is presented in terms of simple logic and should serve to correct misconceptions and avoid future mistakes. We also show a nonlocality proof involving four participants which has interesting theoretical properties.Comment: 8 pages, text clarified, explicit LHV model provided for flawed nonlocality tes

Intrication & non-localité

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal

On the power of non-local boxes

We study quantum information through the use of a virtual two-party device, the nonlocal box. Through the analysis of pseudo-telepathy games, we show the power of the nonlocal box in entanglement simulation. We also show limits on the power of a nonlocal box and propose a generalization for the multi-party scenario. Please see [1] for a full version of the results presented here. Definitions Consider two or more participants that are physically separated and unable to communicate. • We say that the participant’s outputs exhibit nonlocality if there is no classical theory that can explain the correlations. Nonlocality can be achieved, for example, if the participants share quantum entanglement. • Entanglement simulation is the exact reproduction of the correlations of quantum entanglement by participants who do not have access to quantum entanglement. An additional resource, such as communication, is usually required. The nonlocal box The nonlocal box (NLB) is a virtual device shared between two participants, Alice and Bob. When Alice inputs a bit x and Bob inputs a bit y, Alice receives a bit a and Bob a bit b such that: x ∧ y = a ⊕ b. Pseudo-telepathy In a pseudo-telepathy game, two or more players play as a team, against a referee. • The players are physically separated and unable to communicate. • They each receive an input (x ∈ X for Alice, y ∈ Y for Bob). x y NLB a