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We construct $\mathcal{N}=1$ supersymmetric nonlocal theories in four dimension. We discuss higher derivative extensions of chiral and vector superfields, and write down generic forms of K\"ahler potential and superpotential up to quadratic…
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…
A nonlocality anomaly in which a partially entangled state can outperform a maximally entangled state in a task exploiting nonlocality and several ways to remove the anomaly are discussed. A necessary condition for the anomaly to occur is…
In this article, we propose some two-sample tests based on ball divergence and investigate their high dimensional behavior. First, we study their behavior for High Dimension, Low Sample Size (HDLSS) data, and under appropriate regularity…
We discuss possibility of upper-bounding dimension of quantum states device-independently. Provided that the states are pure, it is possible to generate certain four states whose dimension is bounded by two.
We assume that an event caused by a correlation between outcomes of two causally separated measurements is, by definition, a manifestation of quantum nonlocality, or superluminal influence. An example of the Alice-Bob type is given, with…
The possibility that spacetime is extended beyond the familiar 3+1-dimensions has intrigued physicists for a century. Indeed, the consequences of a dimensionally richer spacetime would be profound. Recently, new theories with higher…
If $S$ and $T$ are infinite sequences over a finite alphabet, then the lower and upper mutual dimensions $mdim(S:T)$ and $Mdim(S:T)$ are the upper and lower densities of the algorithmic information that is shared by $S$ and $T$. In this…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
We investigate the problem of detecting dependencies between the components of a high-dimensional vector. Our approach advances the existing literature in two important respects. First, we consider the problem under privacy constraints.…
We prove a Hardy inequality for ultraspherical expansions by using a proper ground state representation. From this result we deduce some uncertainty principles for this kind of expansions. Our result also implies a Hardy inequality on…
We test experimentally the quantum ``paradox'' proposed by Lucien Hardy in 1993 [Phys. Rev. Lett. 71, 1665 (1993)] by using single photons instead of photon pairs. This is achieved by addressing two compatible degrees of freedom of the same…
This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and…
Using a very efficient numerical algorithm of the strong disorder renormalization group method we have extended the investigations about the critical behavior of the random transverse-field Ising model in three and four dimensions, as well…
The standard picture of viable higher-dimensional theories is that extra dimensions manifest themselves at short distances only, their effects being negligible at scales larger than some critical value. We show that this is not necessarily…
A method is presented to construct goodness-of-fit statistics in many dimensions for which the distribution of all possible test results in the limit of an infinite number of data becomes Gaussian if also the number of dimensions becomes…
Recently, Gallego et.al. [Phys. Rev. Lett 107, 210403 (2011)] proved that any future information principle aiming at distinguishing between quantum and post-quantum correlation must be intrinsically multipartite in nature. We establish…
The Fermi paradox is the conflict between an expectation of a high {\em ex ante} probability of intelligent life elsewhere in the universe and the apparently lifeless universe we in fact observe. The expectation that the universe should be…
We generalize the concept of randomness in an infinite binary sequence in order to characterize the degree of randomness by a real number D>0. Chaitin's halting probability \Omega is generalized to \Omega^D whose degree of randomness is…
We prove that multidimensional diffusions in random environment have a limiting velocity which takes at most two different values. Further, in the two-dimensional case we show that for any direction, the probability to escape to infinity in…