A Framework for Quantum-Secure Device-Independent Randomness Expansion

Abstract

A device-independent randomness expansion protocol aims to take an initial random seed and generate a longer one without relying on details of how the devices operate for security. A large amount of work to date has focussed on a particular protocol based on spot-checking devices using the CHSH inequality.Here we show how to derive randomness expansion rates for a wide range of protocols, with security against a quantum adversary. Our technique uses semidefinite programming and a recent improvement of the entropy accumulation theorem. To support the work and facilitate its use, we provide code that can generate lower bounds on the amount of randomness that can be output based on the measured quantities in the protocol. As an application, we give a protocol that robustly generates up to two bits of randomness per entangled qubit pair, which is twice that established in existing analyses of the spot-checking CHSH protocol in the low noise regime.

Efficient randomness certification by quantum probability estimation

“…The conceptual difference between our work and previous works [5,[8][9][10][13][14][15]29] for addressing quantum side information in the device-independent scenario lies in that previous works require quantifying randomness as a function of violations of fixed Bell inequalities before performing security analysis with finite data. Although Bell violations and deviceindependent randomness are related, they are inequivalent quantities: a stronger violation of a fixed Bell inequality does not necessarily certify a larger amount of device-independent randomness [30].…”

“…Many DIRG protocols [3][4][5][6][7][8][9][10][11][12][13][14][15] have been developed in the past ten years. They are different in the following aspects: the specific requirements on quantum devices, the Bell-test configuration applied, the security level achieved, and the asymptotic randomness rate and finite-data efficiency exhibited.…”

“…Besides unsurpassed finite-data efficiency, quantum probability estimation has many other advantages over previous works [5,[8][9][10][13][14][15]29], which include adaptability to changing experimental conditions, flexibility of stopping the experiment early as soon as the prespecified randomness goal is achieved, and tolerance of imperfections in the input distribution. Like entropy accumulation developed in Refs.…”

“…Like entropy accumulation developed in Refs. [13][14][15]29], quantum probability estimation can achieve asymptotically optimal randomness rates and is broadly applicable to both device-independent and device-dependent randomness generation.…”

Towards a realization of device-independent quantum key distribution

“…It is still an open problem whether any other Bell inequality can lead to better performance for DIQKD than the CHSH inequality. Recently, an extensive analysis of the performance of different Bell inequalities for the task of randomness expansion was presented in [120]. For collective attacks, the key ingredients to derive Theorem 2 are the asymptotic equipartition property (Theorem 7) and Lemma 2.…”