[Paper Review] No-signaling-proof randomness extraction from public weak sources

Ravishankar Ramanathan, Michał Banacki+1 more|arXiv (Cornell University)|Aug 19, 2021

Anomaly Detection Techniques and Applications4 citations

TL;DR

This paper presents device-independent and one-sided device-independent randomness amplification protocols for public weak sources using finite devices, achieving security against no-signaling adversaries. It proves that quantum-physical devices can extract nearly uniform randomness from any public ε-SV source with ε < 0.5, while classical no-signaling assumptions allow amplification only for a restricted class of sources, using sequential self-testing of quantum assemblages via steering functionals.

ABSTRACT

The extraction of randomness from weakly random seeds is a topic of central importance in cryptography. Weak sources of randomness can be considered to be either private or public, where public sources such as the NIST randomness beacon broadcast the random bits once they are generated. The problem of device-independent randomness extraction from weak public sources against no-signalling adversaries has remained open. In this paper, we show protocols for device-independent and one-sided device-independent amplification of randomness from weak public Santha Vazirani (SV) sources that use a finite number of devices and are secure against no-signaling adversaries. Specifically, under the assumption that the device behavior is as prescribed by quantum mechanics the protocols allow for amplification of public $ε$-SV sources for arbitrary initial $ε\in [0,0.5)$. On the other hand, when only the assumption of no-signaling between the components of the device is made, the protocols allow for amplification of a limited set of weak public SV sources.

Motivation & Objective

• To develop practical and secure randomness amplification protocols for public weak sources under the no-signaling principle.
• To address the open problem of device-independent randomness extraction from public weak sources against no-signaling adversaries.
• To extend existing frameworks to include one-sided device-independence where one party has trusted quantum devices.
• To demonstrate that quantum resources enable amplification of any public ε-SV source with ε < 0.5, even under minimal assumptions.
• To provide a self-testing framework for sequential quantum assemblages based on steering inequalities, ensuring robustness against no-signaling side information.

Proposed method

• Designs a protocol using sequential measurements on entangled quantum systems to extract randomness from public weak sources.
• Employs a functional $ F_{1, ext{...},n}^{(n)} $ defined over sequential no-signaling assemblages to test for quantum correlations via steering inequalities.
• Uses the maximal value $ 4^n $ of the functional $ F_{1, ext{...},n}^{(n)} $ to certify that the assemblage is a tensor product of individual ideal assemblages $ igotimes_{i=1}^n ho_i $, each self-tested via a local steering functional $ F_i $.
• Applies inductive reasoning to show that if $ F_{1, ext{...},n}^{(n)}( ilde{oldsymbol{ ho}}^{(n)}) = 4^n $, then $ ilde{oldsymbol{ ho}}^{(n)} = igotimes_{i=1}^n ho_i $, where each $ ho_i $ is an inflexible assemblage.
• Establishes that the protocol is secure against no-signaling adversaries by proving that only the correct quantum assemblage achieves the maximal functional value.
• Leverages trusted measurements on one party’s device (1sDI) to perform quantum state tomography and verify the presence of non-local correlations.

Experimental results

Research questions

• RQ1 Can device-independent randomness amplification be achieved from public weak sources under the no-signaling principle?
• RQ2 What class of public weak sources can be amplified when only the no-signaling assumption is made, rather than full quantum mechanics?
• RQ3 Can sequential quantum assemblages be self-tested using steering functionals to certify the presence of genuine quantum correlations?
• RQ4 Is it possible to achieve randomness amplification with a finite number of devices under no-signaling security?
• RQ5 How does one-sided device-independence improve the feasibility and security of randomness extraction from public sources?

Key findings

• The protocol achieves device-independent randomness amplification from any public ε-SV source with ε < 0.5 under the assumption of quantum mechanics.
• When only the no-signaling assumption is made, amplification is possible only for a limited class of public weak sources, not all ε-SV sources.
• The maximal value $ 4^n $ of the functional $ F_{1, ext{...},n}^{(n)} $ is achieved if and only if the sequential assemblage is a tensor product of individual ideal assemblages $ igotimes_{i=1}^n ho_i $, each self-tested via a local steering functional.
• The self-testing result ensures that if $ F_{1, ext{...},n}^{(n)}( ilde{oldsymbol{ ho}}^{(n)}) = 4^n $, then $ ilde{oldsymbol{ ho}}^{(n)} = igotimes_{i=1}^n ho_i $, where each $ ho_i $ is an inflexible assemblage maximizing its respective functional.
• The protocol is robust and secure against no-signaling adversaries, as only the correct quantum assemblage achieves the maximal functional value.
• The framework enables practical randomness extraction using finite devices and is compatible with real-world public sources such as the NIST Randomness Beacon.