On the power of non-local boxes

Abstract

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.

14 pages, 1 figure

References in corpus (7)

• A limit on nonlocality in any world in which communication complexity is not trivial
• The Communication Cost of Simulating Bell Correlations
• Quantum Pseudo-Telepathy
• Quantum entanglement can be simulated without communication
• Entanglement and non-locality are different resources
• Simulating quantum correlations as a distributed sampling problem
• Implausible Consequences of Superstrong Nonlocality

Cited by in corpus (24)

• A limit on nonlocality in any world in which communication complexity is not trivial
• Free randomness can be amplified
• Computational power of correlations
• Entanglement: Quantum or Classical?
• Cloning and Broadcasting in Generic Probabilistic Theories
• Quantum and Super-quantum enhancements to two-sender, two-receiver channels
• Simulation of partial entanglement with nonsignaling resources
• Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory
• No nonlocal box is universal
• Contextuality in multipartite pseudo-telepathy graph games
• Popescu-Rohrlich correlations imply efficient instantaneous nonlocal quantum computation
• Test to separate quantum theory from non-signaling theories
• Correlations constrained by composite measurements
• Extending the Known Region of Nonlocal Boxes that Collapse Communication Complexity
• Generalized Greenberger-Horne-Zeilinger arguments from quantum logical analysis
• Stabilizer states and local realism
• Pseudo-telepathy games and genuine NS k-way nonlocality using graph states
• Non-Local Box Complexity and Secure Function Evaluation
• Quantum strategies for simple 2-player XOR games
• Beating one bit of communication with and without quantum pseudo-telepathy
• Bit Commitment from Weak Non-Locality
• Quantum information and beyond -- with quantum candies
• No nonlocal box with uniform outputs is universal
• Ruling out the class of statistical processes involving two noninteracting identical particles in two modes