Related papers: Free randomness can be amplified
No-Signalling is a fundamental constraint on the probabilistic predictions made by physical theories. It is usually justified in terms of the constraints imposed by special relativity. However, this justification is not as clear-cut as is…
The ultimate random number generators are those certified to be unpredictable -- including to an adversary. The use of simple quantum processes promises to provide numbers that no physical observer could predict but, in practice, unwanted…
The injunction to `analyze the way you randomize' is well-known to statisticians since Fisher advocated for randomization as the basis of inference. Yet even those convinced by the merits of randomization-based inference seldom follow this…
For any finite number of parts, measurements and outcomes in a Bell scenario we estimate the probability of random $N$-qu$d$it pure states to substantially violate any Bell inequality with uniformly bounded coefficients. We prove that under…
Correlations that violate a Bell Inequality are said to be nonlocal, i.e. they do not admit a local and deterministic explanation. Great effort has been devoted to study how the amount of nonlocality (as measured by a Bell inequality…
Non-deterministic random bits are needed in many scientific fields. Unfortunately today's computers are very limited in ability to produce them. We present here a method for extraction of non-deterministic random bits from random physics…
Cryptography depends on truly unpredictable numbers, but physical sources emit biased or correlated bits. Quantum mechanics enables the amplification of imperfect randomness into nearly perfect randomness, but prior demonstrations have…
A local and deterministic model of quantum correlations is always possible, as shown explicitly by Brans in 1988: one simply needs the physical systems being measured to have a suitable statistical correlation with the physical systems…
With Bell's inequalities one has a formal expression to show how essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a simple experimental arrangement. For the case of…
This paper studies one-sided hypothesis testing under random sampling without replacement. That is, when $n+1$ binary random variables $X_1,\ldots, X_{n+1}$ are subject to a permutation invariant distribution and $n$ binary random variables…
One of the most striking features of quantum theory is that it allows distant observers to share correlations that resist local hidden variable (classical) explanations, a phenomenon referred to as Bell nonlocality. Besides their…
Bell gave the now standard definition of a local hidden variable theory and showed that such theories cannot reproduce the predictions of quantum mechanics without violating his ``free will'' criterion: experimenters' measurement choices…
Random numbers are indispensable for a variety of applications ranging from testing physics foundation to information encryption. In particular, nonlocality tests provide a strong evidence to our current understanding of nature -- quantum…
We study the question, ``For which reals $x$ does there exist a measure $\mu$ such that $x$ is random relative to $\mu$?'' We show that for every nonrecursive $x$, there is a measure which makes $x$ random without concentrating on $x$. We…
The generation of series of random numbers is an important and difficult problem. Appropriate measurements on entangled states have been proposed as the definitive solution, based on the impossibility of exploiting quantum non locality to…
We show that Bell correlations may arise as a special sort of selection artefact, produced by ordinary control of the initial state of the experiments concerned. This accounts for nonlocality, without recourse to any direct spacelike…
This work starts from definition of randomness, the results of algorithmic randomness are analyzed from the perspective of application. Then, the source and nature of randomness is explored, and the relationship between infinity and…
We introduce the notion of a random mean generated by a random variable and give a construction of its expected value. We derive some sufficient conditions under which strong laws of large numbers and some limit theorems hold for random…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
Quantum technologies offer significant advancements in information processing and communication, notably in the domain of random number generation (RNG). The use of Bell inequalities enables users to certify the randomness of outputs…