Device-independent randomness generation with sublinear shared quantum resources

Abstract

In quantum cryptography, deviceindependent (DI) protocols can be certified secure without requiring assumptions about the inner workings of the devices used to perform the protocol. In order to display nonlocality, which is an essential feature in DI protocols, the device must consist of at least two separate components sharing entanglement. This raises a fundamental question: how much entanglement is needed to run such DI protocols? We present a two-device protocol for DI random number generation (DIRNG) which produces approximately n bits of randomness starting from n pairs of arbitrarily weakly entangled qubits. We also consider a variant of the protocol where m singlet states are diluted into n partially entangled states before performing the first protocol, and show that the number m of singlet states need only scale sublinearly with the number n of random bits produced. Operationally, this leads to a DIRNG protocol between distant laboratories that requires only a sublinear amount of quantum communication to prepare the devices.

Self-testing of quantum systems: a review

“…The results on self-testing properties of binary XOR games from [MS13] were expanded in [MS16] and used to devise protocols for exponential randomness expansion. More recently, the authors of [BMP18] directly use robust selftesting bounds for the tilted-CHSH inequality [BP15] to lower bound the randomness generated in their protocol. Self-testing techniques are also used in [APVW16, ABDC18, WKB + 19] to prove that two bits of local randomness can be certified from a two-qubit entangled state.…”

Quantum violations in the Instrumental scenario and their relations to the Bell scenario

“…For instance, the tilted CHSH inequalities introduced in [41], though weaker than the CHSH inequality for detecting non-classicality, are useful for other purposes. In a device-independent setting, they enable certifying more randomness that would be possible using standard CHSH [41,42].…”

No Bipartite-Nonlocal Causal Theory Can Explain Nature's Correlations

“…An important property of Bell inequalities is that any violation implies true randomness [16,47]. In our case, A 1 B 1 reaches the maximal algebraic violation of CHSH, which implies that A 1 (and also B 1 ) is totally unpredictable.…”