Related papers: Time series, correlation matrices and random matri…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
Temporal quantum correlations provide an intriguing way of testing quantumness at the macroscopic level, with a logical hierarchy present among the quantum correlations associated with nonmacrorealism, temporal steering, and temporal…
Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an…
The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor in interacting chaotic few- and many-body systems,…
Reference frames are used to parameterize measurements of physical effects, but since their practical realization uses material objects, they may affect observations performed in a combined quantum state of the measured system together with…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
The results of space-like separated measurements are independent of distant measurement settings, a property one might call two-way no-signalling. In contrast, time-like separated measurements are only one-way no-signalling since the past…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
Time series forecasting has always been a thought-provoking topic in the field of machine learning. Machine learning scientists define a time series as a set of observations recorded over consistent time steps. And, time series forecasting…
The verification and quantification of experimentally created entanglement by simple measurements, especially between distant particles, is an important basic task in quantum processing. When composite systems are subjected to local…
Because of the rotational components on quantum circuits, some quantum neural networks based on variational circuits can be considered equivalent to the classical Fourier networks. In addition, they can be used to predict the Fourier…
Time-dependent response and correlation functions are studied in random quantum systems composed of infinitely many parts without mutual interaction and defined with statistically independent random matrices. The latter are taken within the…
Chain-mapping techniques in combination with the time-dependent density matrix renormalization group are a powerful tool for the simulation of open-system quantum dynamics. For finite-temperature environments, however, this approach suffers…
Many theories are formulated as constrained systems. We provide a mechanism that explains the origin of physical states of a constrained system by a process of selection of noiseless subsystems when the system is coupled to an external…
Relativistic quantum information combines the informational approach to understanding and using quantum mechanics systems - quantum information - with the relativistic view of the universe. In this introductory review we examine key results…
The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this…