Related papers: Ideal stochastic process modeling with post-quantu…
The uncertainty principle is an important principle in quantum theory. Based on this principle, it is impossible to predict the measurement outcomes of two incompatible observables, simultaneously. Uncertainty principle basically is…
It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…
The detection and quantification of non-Markovianity, a.k.a. memory, in quantum systems is a central problem in the theory of open quantum systems. There memory is as a result of the interaction between the system and its environment.…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
Minimizing cross-entropy is a widely used method for training artificial neural networks. Many training procedures based on backpropagation use cross-entropy directly as their loss function. Instead, this theoretical essay investigates a…
Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously…
We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model both in Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the…
Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations.…
The excess work required to drive a stochastic system out of thermodynamic equilibrium through a time-dependent external perturbation is directly related to the amount of entropy produced during the driving process, allowing excess work and…
We formulate a semi-classical circuit model to clarify the role of quantum entanglement in the recently discovered encoding phase transitions in quantum circuits with measurements. As a starting point we define a random circuit model with…
Stochastic dominance serves as a general framework for modeling a broad spectrum of decision preferences under uncertainty, with risk aversion as one notable example, as it naturally captures the intrinsic structure of the underlying…
Uncertainty principle has a fundamental role in quantum theory. This principle states that it is not possible to measure two incompatible observers simultaneously. The uncertainty principle is expressed logically in terms of standard…
We consider an ideal experiment in which unlimited nonprojective quantum measurements are sequentially performed on a system that is initially entangled with a distant one. At each step of the sequence, the measurements are randomly chosen…
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability…
We show how the shared information between the past and future---the excess entropy---derives from the components of directional information stored in the present---the predictive and retrodictive causal states. A detailed proof allows us…
The aim of the article is to develop the stochastic interpretation of quantum mechanics by E. Nelson on the basis of balancing the intra-systemic contradiction (i.e., antisymmetry) between "order" and "chaos". For the set task, it is…
Accurate information processing is crucial both in technology and in nature. To achieve it, any information processing system needs an initial supply of resources away from thermal equilibrium. Here we establish a fundamental limit on the…
The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to…
Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…