Quantum correlations cannot be reproduced with a finite number of measurements in any no-signaling theory

Abstract

We show, for any finite $n\ge 2$, that there exist quantum correlations obtained from performing $n$ dichotomic quantum measurements in a bipartite Bell scenario, which cannot be reproduced by mixtures of measurement devices with at most $(n-1)$ incompatible measurements across different partitions in any no-signaling theory. That is, it requires any no-signaling theory an unbounded number of measurements to reproduce the predictions of quantum theory. We prove our results by showing that there exist linear Bell inequalities that have to be obeyed by any no-signaling theory involving only $(n-1)$-wise incompatible measurements and show explicitly how these can be violated in quantum theory. Finally, we discuss the relation of our work to previous works ruling out alternatives to quantum theory with some kind of bounded degree of freedom and consider the experimental verifiability of our results.

7+5 pages, 1 figure. Close to published version

References in corpus (16)

• Device-independent security of quantum cryptography against collective attacks
• Bounding the set of quantum correlations
• Private Randomness Expansion With Untrusted Devices
• A derivation of quantum theory from physical requirements
• Quantum theory based on real numbers can be experimentally falsified
• Almost quantum correlations
• Grothendieck's constant and local models for noisy entangled quantum states
• Incompatible measurements in quantum information science
• Higher-order interference and single-system postulates characterizing quantum theory
• General probabilistic theories: An introduction
• Notes on Joint Measurability of Quantum Observables
• Direct Bound-Electron $g$ factor Difference Measurement with Coupled Ions
• All measurements in a probabilistic theory are compatible if and only if the state space is a simplex
• Device-independent quantification of measurement incompatibility
• Generalizations of Boxworld
• Distributed quantum incompatibility