Nonlocality and True Randomness

Steven Weinstein

Hong-Wei Li, Marcin Pawłowski, Ramij Rahaman +2 more

In this work, we propose device-independent true random number expansion protocols based on noninequality paradoxes such as Hardy's and Cabello's nonlocality arguments, thus highlighting the noninequality paradox as an important resource for device-independent quantum-information processing, in particular for generating true randomness. As a byproduct, we find that the nonlocal bound of the Cabello argument with arbitrary dimension is the same as the one achieved in the qubits system. More interestingly, we propose a dimension witness paradox based on the Cabello argument which can be used for constructing a semi--device-independent true random number expansion protocol.

J. S. Bell

Nicolas Gisin

It is argued that realism and true randomness are fully compatible. Realistic true random events are acts of pure creation that obey strict laws, but do not necessarily satisfy Kolmogorov's axioms of probabilities. Realistic true randomness is some sort of nondeterministic force, or propensity of physical systems to manifest such and such properties under such and such conditions. Realistic random events reflect preexisting properties, as required by realism, simply the reflection is not deterministic; still, the preexisting properties determine the propensities of the different possible events. It is argued that deterministic extensions of quantum physics are necessarily incompatible with special relativity. Hence, from today's violations of Bell's inequalities one can conclude that all future physics theories will display true randomness as does quantum physics. It is argued that accepting true randomness and realism leads to new questions with interesting answers, allowing one 1) to study nonlocality in configurations with many independent sources and 2) to bound how much free will is needed for a proper violation of Bell's inequality.

Виктор Степанович Доценко

Chao Zhang, Yi Li, Xiao-Min Hu +7 more

Device-independent randomness certification based on Bell nonlocality does not require any assumptions about the devices, thus provides adequate security. Great effort has been made to demonstrate that nonlocality is necessary for generating quantum randomness, but the minimal resource required has not been clarified. Here we prove and experimentally demonstrate that violating any two-input Bell inequality is both necessary and sufficient for certifying randomness, however, for the multiple-input cases, this sufficiency ceases to apply, leading to certain states exhibiting Bell nonlocality without the capability to certify randomness. We examine two typical classes of Bell inequalities with multiple input and multiple output, the facet inequalities and Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio inequalities, in the high-dimensional photonic system, and observe that the violation of the latter one can always certify randomness which is not true for the former. The private randomness with a generation rate of 1.867±0.018 bits per photon pair is obtained in the scenario of Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio inequalities with 3-input and 4-output. Our Letter unravels the internal connection between randomness and nonlocality, effectively enhancing the performance of tasks such as device-independent random number generation.