Related papers: The myth of equidistribution for high-dimensional …
We have introduced in former work the concept of Deep Randomness and its interest to design Unconditionally Secure communication protocols. We have in particular given an example of such protocol and introduced how to design a Deep Random…
Linear-feedback shift register (LFSR) based pseudo-random number generator (PRNG) has applications in a plethora of fields. The issue of being linear is generally circumvented by introducing non-linearities as per the required applications,…
To improve accuracy and speed of regressions and classifications, we present a data-based prediction method, Random Bits Regression (RBR). This method first generates a large number of random binary intermediate/derived features based on…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
This article considers the generative modeling of the (mixed) states of quantum systems, and an approach based on denoising diffusion model is proposed. The key contribution is an algorithmic innovation that respects the physical nature of…
This is the documentation for generating random samples from the quantum state space in accordance with a specified distribution, associated with this webpage: http://tinyurl.com/QSampling . Ready-made samples (each with at least a million…
The random number generators (RNGs) are an indispensable tool in cryptography. Of various types of RNG method, those using radiations from nuclear decays (radioactive RNG) has a relatively long history but their security has never been…
We develop a method for the random sampling of (multimode) Gaussian states in terms of their covariance matrix, which we refer to as a random quantum covariance matrix (RQCM). We analyze the distribution of marginals and demonstrate that…
Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…
The dramatic increase in the efficiency of a quantum computer over a classical computer, raises a natural question asking, how much of this success could be attributed to its quantum nature and how much to its probabilistic content. To…
The resource theory of imaginarity studies the operational value of imaginary parts in quantum states, operations, and measurements. Here we introduce and study the distillation and conversion of imaginarity in distributed scenario. This…
We describe random processes (with binary alphabet) whose entropy is less than 1 (per letter), but they mimic true random process, i.e., by definition, generated sequence can be interpreted as the result of the flips of a fair coin with…
Emerging communication and cryptography applications call for reliable, fast, unpredictable random number generators. Quantum random number generation (QRNG) allows for the creation of truly unpredictable numbers thanks to the inherent…
The selection of random subspaces plays a role in quantum information theory analogous to the role of random strings in classical information theory. Recent applications have included protocols achieving the quantum channel capacity and…
In every state of a quantum particle, Wigner's quasidistribution is the unique quasidistribution on the phase space with the correct marginal distributions for position, momentum, and all their linear combinations.
This paper explores the development and viability of an alternative pseudorandom number generator (PRNG) that leverages the chaotic dynamics of multiple pendulum systems. Some traditional PRNGs, notably the one implemented in the…
For distributions $\mathbb{P}$ and $\mathbb{Q}$ with different supports or undefined densities, the divergence $\textrm{D}(\mathbb{P}||\mathbb{Q})$ may not exist. We define a Spread Divergence $\tilde{\textrm{D}}(\mathbb{P}||\mathbb{Q})$ on…
The concept of randomness plays an important role in many disciplines. On one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other hand, randomness is a resource for cryptography,…
A pseudorandom quantum state (PRS) is an ensemble of quantum states indistinguishable from Haar-random states to observers with efficient quantum computers. It allows one to substitute the costly Haar-random state with efficiently…