Related papers: Pseudorandomness Properties of Random Reversible C…

This paper investigates a joint source-channel secrecy problem for the Shannon cipher broadcast system. We suppose list secrecy is applied, i.e., a wiretapper is allowed to produce a list of reconstruction sequences and the secrecy is…

Given a symmetric $n\times n$ matrix $P$ with $0 \le P(u, v)\le 1$, we define a random graph $G_{n, P}$ on $[n]$ by independently including any edge $\{u, v\}$ with probability $P(u, v)$. For $k\ge 1$ let $\mathcal{A}_k$ be the property of…

For Boolean functions computed by read-once, depth-$D$ circuits with unbounded fan-in over the de Morgan basis, we present an explicit pseudorandom generator with seed length $\tilde{O}(\log^{D+1} n)$. The previous best seed length known…

We prove that $poly(t) \cdot n^{1/D}$-depth local random quantum circuits with two qudit nearest-neighbor gates on a $D$-dimensional lattice with n qudits are approximate $t$-designs in various measures. These include the "monomial"…

Zigzags in graphs embedded in surfaces are cyclic sequences of edges whose any two consecutive edges are different, have a common vertex and belong to the same face. We investigate zigzags in randomly constructed combinatorial tetrahedral…

We consider a class of random permutations of the interval $[-n,n]$, in which points are typically displaced a distance $O(W)$. We show the cycles are localized on the scale $W^3$, with an exponentially decaying tail bound. Analogous to…

Say that a permutation of $1,2,\ldots,n$ is \textit{$k$-bounded} if every pair of consecutive entries in the permutation differs by no more than $k$. Such a permutation is \textit{anchored} if the first entry is $1$ and the last entry is…

We consider stochastic differential equations, obtained by adding weak Gaussian white noise to ordinary differential equations admitting $N$ asymptotically stable periodic orbits. We construct a discrete-time, continuous-space Markov chain,…

Sub-categories of mathematical topology, like the mathematical theory of chaos, offer interesting applications devoted to information security. In this research work, we have introduced a new chaos-based pseudorandom number generator…

We obtain lower tail estimates for the smallest singular value of random matrices with independent but non-identically distributed entries. Specifically, we consider $n\times n$ matrices with complex entries of the form \[ M = A\circ X + B…

Let $n$ be a positive integer divisible by 8. The Clifford-cyclotomic gate set $\mathcal{G}_n$ consists of the Clifford gates, together with a $z$-rotation of order $n$. It is easy to show that, if a circuit over $\mathcal{G}_n$ represents…

A permutation of [n] induces a graph on [n] such that the edges of the graph correspond to inversion pairs of the permutation. This graph is connected if and only if the corresponding permutation is indecomposable. Let s(n,m) denote a…

We conduct a systematic study of quantum circuits composed of multiple-control $Z$-rotation (MCZR) gates as primitives, since they are widely-used components in quantum algorithms and also have attracted much experimental interest in recent…

We consider a family X^{(n)}, n \in \bbN_+, of continuous-time nearest-neighbor random walks on the one dimensional lattice Z. We reduce the spectral analysis of the Markov generator of X^{(n)} with Dirichlet conditions outside (0,n) to the…

We consider three different models of sparse random graphs:~undirected and directed Erd\H{o}s-R\'{e}nyi graphs, and random bipartite graph with an equal number of left and right vertices. For such graphs we show that if the edge…

Reversible circuits have applications in digital signal processing, computer graphics, quantum computation and cryptography. In this paper, a generalized k*k reversible gate family is proposed and a 3*3 gate of the family is discussed.…

Decoupling has become a central concept in quantum information theory with applications including proving coding theorems, randomness extraction and the study of conditions for reaching thermal equilibrium. However, our understanding of the…

Let $S_n$ be the symmetric group of all permutations of $\{1, \cdots, n\}$ with two generators: the transposition switching $1$ with $2$ and the cyclic permutation sending $k$ to $k+1$ for $1\leq k\leq n-1$ and $n$ to $1$ (denoted by…

We study the problem of reaching agreement in a synchronous distributed system by $n$ autonomous parties, when the communication links from/to faulty parties can omit messages. The faulty parties are selected and controlled by an adaptive,…

We present two deterministic algorithms to approximate single-qutrit gates. These algorithms utilize the Clifford + $\mathbf{R}$ group to find the best approximation of diagonal rotations. The first algorithm exhaustively searches over the…