Consequences and limits of nonlocal strategies

@article{Cleve2004ConsequencesAL,
  title={Consequences and limits of nonlocal strategies},
  author={Richard Cleve and Peter H{\o}yer and Ben Toner and John Watrous},
  journal={Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.},
  year={2004},
  pages={236-249}
}
  • R. Cleve, P. Høyer, J. Watrous
  • Published 12 April 2004
  • Mathematics
  • Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.
This paper investigates various aspects of the nonlocal effects that can arise when entangled quantum information is shared between two parties. A natural framework for studying nonlocality is that of cooperative games with incomplete information, where two cooperating players may share entanglement. Here, nonlocality can be quantified in terms of the values of such games. We review some examples of non-locality and show that it can profoundly affect the soundness of two-prover interactive… 

Figures from this paper

Classification and Computability for Nonlocal Games
TLDR
This work attempts to relate the two models, namely XOR games and linear system games, by studying the relationships between their strategies and refutations, and tries to understand when results for one model can be transferred to the other.
On deciding the existence of perfect entangled strategies for nonlocal games
TLDR
This work considers the problem of deciding whether a nonlocal game admits a perfect entangled strategy that uses projective measurements on a maximally entangled shared state and shows that independent set games are the hardest instances of this problem.
Classical, Quantum and Non-signalling Resources in Bipartite Games
TLDR
This work shows that every pseudo-telepathy game yields both a proof of the Bell-Kochen-Specker theorem and an instance of a two-prover interactive proof system that is classically sound, but that becomes unsound when provers use shared entanglement.
Extended Nonlocal Games
TLDR
This thesis builds up the framework for extended nonlocal games, a mathematical framework that abstractly models a physical system and studies their properties and how they relate to non local games.
Classical Interaction Cannot Replace Quantum Nonlocality
We present a two-player communication task that can be solved by a protocol of polylogarithmic cost in the simultaneous message passing model with classical communication and shared entanglement, but
Quantum entanglement: insights via graph parameters and conic optimization
TLDR
This thesis proposes a novel approach to the study of these quantum graph parameters using the paradigm of conic optimization, and introduces and study the completely positive semidefinite cone, a new matrix cone consisting of all symmetric matrices that admit a Gram representation by positive semidfinite matrices.
Extended non-local games and monogamy-of-entanglement games
TLDR
It is proved that a natural extension of the Navascués–Pironio–Acín hierarchy of semidefinite programmes converges to the optimal commuting measurement value of extended non-local games, and two extensions of results of Tomamichel et al. concerning monogamy-of-entanglement games are proved.
Nonlocal games, synchronous correlations, and Bell inequalities.
A nonlocal game with a synchronous correlation is a natural generalization of a function between two finite sets, and has recently appeared in the context of quantum graph homomorphisms. In this work
Survey on Nonlocal Games and Operator Space Theory
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which
A generalized Grothendieck inequality which lower bounds the entanglement required to play nonlocal games
Suppose that Alice and Bob make local two-outcome measurements on a shared entangled quantum state. We show that, for all positive integers d, there exist correlations that can only be reproduced if
...
...

References

SHOWING 1-10 OF 84 REFERENCES
Nonlocality and the Kochen-Specker paradox
A new proof of the impossibility of reconciling realism and locality in quantum mechanics is given. Unlike proofs based on Bell's inequality, the present work makes minimal and transparent use of
Cost of Exactly Simulating Quantum Entanglement with Classical Communication
TLDR
It is shown that, in the case of a single pair of qubits in a Bell state, a constant number of bits of communication is always sufficient — regardless of the number of measurements under consideration.
The impossibility of pseudotelepathy without quantum entanglement
TLDR
This work provides the proof that communication is indeed necessary to win with certainty if no quantum entanglement is shared by the players, and completes the game's analysis and shows its "pseudotelepathic" properties.
A new protocol and lower bounds for quantum coin flipping
TLDR
A new protocol is presented and two lower bounds for quantum coin flipping are presented that show that no dishonest party can achieve one outcome with probability more than 0.75 and that if a protocol achieves a bias of at most epsilon, it must use at least at least three rounds of communication.
Quantum analogues of the Bell inequalities. The case of two spatially separated domains
One Investigates inequalities for the probabilities and mathematical expectations which follow from the postulates of the local quantum theory. It turns out that the relation between the quantum and
The Problem of Hidden Variables in Quantum Mechanics
Forty years after the advent of quantum mechanics the problem of hidden variables, that is, the possibility of imbedding quantum theory into a classical theory, remains a controversial and obscure
Quantum vs. classical communication and computation
TLDR
A simple and general simulation technique is presented that transforms any black-box quantum algorithm to a quantum communication protocol for a related problem, in a way that fully exploits the quantum parallelism, to obtain new positive and negative results.
On the Einstein-Podolsky-Rosen Paradox
Tests of Bell inequalities
Multi-prover interactive proofs: how to remove intractability assumptions
TLDR
It is proved that all NP languages have perfect zero-knowledge proof-systems in this model, without making any intractability assumptions, and its properties and applicability to cryptography are examined.
...
...