No quantum realization of extremal no-signaling boxes

Abstract

Pure states are very important in any theory since they represent states of maximal information about the system within the theory. Here, we show that no non-trivial (not local realistic) extremal states (boxes) of general no-signaling theories can be realized within quantum theory. We then explore three interesting consequences of this fact. Firstly, since the pure states are uncorrelated from the environment, the statement forms a no-go result against the most straightforward device-independent protocol for randomness or secure key generation against general no-signaling adversaries. It also leads to the interesting question whether all non-extremal boxes allow for non-local correlations with the adversary. Secondly, in addition to the fact that new information-theoretic principles (designed to pick out the set of quantum correlations from among all non signaling ones) can in consequence be tested on arbitrary non-local vertices to check their validity, it also allows the possibility of excluding from the quantum set any box of no-signaling correlations that can be distilled to a non-local vertex. Finally, it also forms a sufficient condition to identify non-local games with no quantum winning strategy, when one can show that the game has a single unique non-signaling winning strategy. We illustrate each of these consequences with the example of generalized Popescu-Rohrlich boxes.

8 pages

References in corpus (7)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Graph-Theoretic Approach to Quantum Correlations
• Almost quantum correlations
• Simple explanation of the quantum violation of a fundamental inequality
• Non-locality distillation and post-quantum theories with trivial communication complexity
• Generalized XOR games with $d$ outcomes and the task of non-local computation
• Simple conditions constraining the set of quantum correlations

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• Equivalence between face nonsignaling correlations, full nonlocality, all-versus-nothing proofs, and pseudotelepathy
• Amplifying the randomness of weak sources correlated with devices
• Learning optimal quantum models is NP-hard
• All two-party facet Bell inequalities are violated by Almost Quantum correlations
• Generalised Mermin-type non-locality arguments
• On the edge of the set of no-signaling assemblages
• (Almost-)Quantum Bell Inequalities and Device-Independent Applications
• Single trusted qubit is necessary and sufficient for quantum realisation of extremal no-signaling correlations
• Hybrid no-signaling-quantum correlations