Related papers: Generating k-independent variables in constant tim…
We show that the inverse limit of the graded algebras of local unitary invariant polynomials of finite dimensional k-partite quantum systems is free, and give an algebraically independent generating set. The number of degree 2d invariants…
We use separation of variables as a tool to identify and to analyze exactly soluble time-dependent quantum mechanical potentials. By considering the most general possible time-dependent re-definition of the spatial coordinate, as well as…
Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of…
A random number generator is proposed based on a theorem about existence of chaos in fixed point iteration of x= cot2(x). Digital computer simulation of this function iteration exhibits random behavior. A method is proposed to extract…
This paper investigates the usage of generating functions (GFs) encoding measures over the program variables for reasoning about discrete probabilistic programs. To that end, we define a denotational GF-transformer semantics for…
In this paper, we establish a local limit theorem for linear fields of random variables constructed from independent and identically distributed innovations each with finite second moment. When the coefficients are absolutely summable we do…
Goldreich suggested candidates of one-way functions and pseudorandom generators included in $\mathsf{NC}^0$. It is known that randomly generated Goldreich's generator using $(r-1)$-wise independent predicates with $n$ input variables and…
The generation of random numbers is a task of paramount importance in modern science. A central problem for both classical and quantum randomness generation is to estimate the entropy of the data generated by a given device. Here we present…
We develop a quantum version of the probability estimation framework [arXiv:1709.06159] for randomness generation with quantum side information. We show that most of the properties of probability estimation hold for quantum probability…
We present a scheme for a self-testing quantum random number generator. Compared to the fully device-independent model, our scheme requires an extra natural assumption, namely that the mean energy per signal is bounded. The scheme is…
Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a…
We study a natural variant of scheduling that we call \emph{partial scheduling}: In this variant an instance of a scheduling problem along with an integer $k$ is given and one seeks an optimal schedule where not all, but only $k$ jobs, have…
A quantum random number generator (QRNG) based on gated single photon detection of an InGaAs photodiode at GHz frequency is demonstrated. Owing to the extremely long coherence time of each photon, each photons' wavefuntion extends over many…
The time-dependent variational principle is used to optimize the linear and nonlinear parameters of Gaussian basis functions to solve the time-dependent Schrodinger equation in 1 and 3 dimensions for a one-body soft Coulomb potential in a…
We propose a new approach to nondeterministic random number generation. In theory, the randomness originated from the uncorrelated nature of consecutive laser pulses with Poissonian photon number distribution and that of the consecutive…
Let $\mathbf{A}_{n,m;k}$ be a random $n \times m$ matrix with entries from some field $\mathbb{F}$ where there are exactly $k$ non-zero entries in each column, whose locations are chosen independently and uniformly at random from the set of…
We propose a training-free quantum generative paradigm, which is fundamentally different from current generative models, which demand substantial computational power, face practical scalability limits, and often function as opaque black…
A polynomial threshold function (PTF) $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a function of the form $f(x) = \mathsf{sign}(p(x))$ where $p$ is a polynomial of degree at most $d$. PTFs are a classical and well-studied complexity class…
A polynomial-time algorithm for computing the permanent in any field of characteristic 3 is presented in this article. The principal objects utilized for that purpose are the Cauchy and Vandermonde matrices, the discriminant function and…
We present efficient computational solutions to the problems of checking equality, performing multiplication, and computing minimal representatives of elements of free bands. A band is any semigroup satisfying the identity $x ^ 2 \approx x$…