Related papers: Correlation, Linear Complexity, Maximum order Comp…
How can we characterize different types of correlation between quantum systems? Since correlations cannot be generated locally, we take any real function of a multipartite state which cannot increase under local operations to measure a…
We present an analysis of eight measures used for quantifying morphological complexity of natural languages. The measures we study are corpus-based measures of morphological complexity with varying requirements for corpus annotation. We…
Quantum systems generally exhibit different kinds of correlations. In order to compare them on equal footing, one uses the so-called distance-based approach where different types of correlations are captured by the distance to different…
In the context of the Oppenheim-Horodecki paradigm of nonclassical correlation, a bipartite quantum state is (properly) classically correlated if and only if it is represented by a density matrix having a product eigenbasis. On the basis of…
Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in…
In this paper, a new method is presented to compute the 2-adic complexity of pseudo-random sequences. With this method, the 2-adic complexities of all the known sequences with ideal 2-level autocorrelation are uniformly determined. Results…
The linear complexity and the $k$-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By studying the linear complexity of binary…
The purpose of this short tutorial paper is to review various criteria that have been used to characterize the quantum character of correlations in optical systems, such as "gemellity", QND correlation, intrication, EPR correlation and Bell…
The quantumness of the correlation known as quantum correlation is usually measured by quantum discord. So far various quantum discords can be roughly understood as indirect measure by some special discrepancy of two quantities. We present…
Coherence and correlations represent two related properties of a compound system. The system can be, for instance, the polarization of a photon, which forms part of a polarization-entangled two-photon state, or the spatial shape of a…
The hierarchy of correlations is an analytical approximation method which allows us to study non-equilibrium phenomena in strongly interacting quantum many-body systems on lattices in higher dimensions. So far, this method was restricted to…
Binary search finds a given element in a sorted array with an optimal number of $\log n$ queries. However, binary search fails even when the array is only slightly disordered or access to its elements is subject to errors. We study the…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion…
$k$-level correlation is a local statistic of sequences modulo 1, describing the local spacings of $k$-tuples of elements. For $k = 2$ this is also known as pair correlation. We show that there exists a well spaced increasing sequence of…
This paper addresses the problem of quickest detection of a change in the maximal coherence between columns of a $n\times p$ random matrix based on a sequence of matrix observations having a single unknown change point. The random matrix is…
In this paper, we empirically investigate correlations among four centrality measures, originated from the social science, of various complex networks. For each network, we compute the centrality measures, from which the partial correlation…
We provide a protocol to measure out-of-time-order correlation functions. These correlation functions are of theoretical interest for diagnosing the scrambling of quantum information in black holes and strongly interacting quantum systems…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
We measure and compare three correlation lengths proposed to describe the extent of structural order in amorphous systems. In particular, the recently proposed "patch correlation length" is measured as a function of temperature and…