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Random numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell test experiment for the generation of randomness that cannot be predicted within any physical theory that allows one to make independent measurement choices and prohibits superluminal signaling. To certify and quantify the randomness, we describe a new protocol that performs well in an experimental regime characterized by low violation of Bell inequalities. Applying an extractor function to our data, we obtained 256 new random bits, uniform to within 0.001.
From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challe
Randomness is a fundamental feature in nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathemati
Randomness is fundamental in quantum theory, with many philosophical and practical implications. In this paper we discuss the concept of algorithmic randomness, which provides a quantitative method to assess the Borel normality of a given sequence of
A new causal paradox in superluminal signaling is presented. In contrast to the Tolman paradox with tachyon exchange between two parties, the new paradox appears already in a one-way superluminal signaling, even without creating the time loop. This p
We propose a framework to build formal developments for robot networks using the COQ proof assistant, to state and to prove formally various properties. We focus in this paper on impossibility proofs, as it is natural to take advantage of the COQ hig