Related papers: On the concept of complexity in random dynamical s…
The complexity of the quantum state of a multiparticle system and the maximum possible accuracy of its quantum description are connected by a relation similar to the coordinate-momentum uncertainty relation. The coefficient in this relation…
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
We analyze the consequences of iterative measurement-induced nonlinearity on the dynamical behavior of qubits. We present a one-qubit scheme where the equation governing the time evolution is a complex-valued nonlinear map with one complex…
We propose to examine the predictability and the complexity characteristics of the Standard&Poor500 dynamics behaviors in a coarse-grained way using the symbolic dynamics method and under the prism of the Information theory through the…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
We introduce the concept of {\em information compressibility}, $K_I$, which measures the relative change of number of available microstates of an open system in response to an energy variation. We then prove that at the time in which the…
Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the entropy by the…
Instead of static entropy we assert that the Kolmogorov complexity of a static structure such as a solid is the proper measure of disorder (or chaoticity). A static structure in a surrounding perfectly-random universe acts as an interfering…
The Kolmogorov-Sinai (K-S) entropy is a central measure of complexity and chaos. Its calculation for many-body systems is an interesting and important challenge. In this paper, the evaluation is formulated by considering $N$-dimensional…
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…
Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity" we use an information theory approach to formulate general measures of systems complexity. We examine the properties of…
The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…
Simple dynamical systems -- with a small number of degrees of freedom -- can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of…
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…
We consider unitary dynamical evolutions on n qubits caused by time dependent pair-interaction Hamiltonians and show that the running time of a parallelized two-qubit gate network simulating the evolution is given by the time integral over…
Here, we propose a new tool to estimate the complexity of a time series: the entropy of difference (ED). The method is based solely on the sign of the difference between neighboring values in a time series. This makes it possible to…