Randomness vs Non Locality and Entanglement

TL;DR

This paper explores the relationship between quantum non-locality, entanglement, and randomness, showing that near-maximal randomness can be certified even with minimal violations of Bell inequalities or low entanglement.

Contribution

It demonstrates that high randomness certification is possible with correlations that only slightly violate Bell inequalities or have little entanglement, challenging previous assumptions.

Findings

Near-maximal randomness can be certified with minimal Bell violation.

Almost-local correlations can achieve optimal randomness generation.

Low entanglement states can still produce near-maximal randomness.

Abstract

According to quantum theory, the outcomes obtained by measuring an entangled state necessarily exhibit some randomness if they violate a Bell inequality. In particular, a maximal violation of the CHSH inequality guarantees that 1.23 bits of randomness are generated by the measurements. However, by performing measurements with binary outcomes on two subsystems one could in principle generate up to two bits of randomness. We show that correlations that violate arbitrarily little the CHSH inequality or states with arbitrarily little entanglement can be used to certify that close to the maximum of two bits of randomness are produced. Our results show that non-locality, entanglement, and the amount of randomness that can be certified in a Bell-type experiment are inequivalent quantities. From a practical point of view, they imply that device-independent quantum key distribution with optimal key generation rate is possible using almost-local correlations and that device-independent randomness generation with optimal rate is possible with almost-local correlations and with almost-unentangled states.