Related papers: Optimality and Complexity in Measured Quantum-Stat…
We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation." Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time…
The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is…
A quantum stochastic model for an open dynamical system (quantum receiver) and output multi-channel of observation with an additive nonvacuum quantum noise is given. A quantum stochastic Master equation for the corresponding instrument is…
Quantum measurements are crucial to observe the properties of a quantum system, which however unavoidably perturb its state and dynamics in an irreversible way. Here we study the dynamics of a quantum system while being subject to a…
Computer science theory provides many different measures of complexity of a system including Kolmogorov complexity, logical depth, computational depth, and Levin complexity. However, these measures are all defined only for deterministic…
Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…
We demonstrate that temporal observables, which are sensitive to a system's history (as opposed to its state), implicate entangled histories. We exemplify protocols for measuring such observables, and algorithms for predicting the…
We describe in a qualitative way a possible picture of the Measurement Process in Quantum Mechanics, which takes into account: 1. the finite and non zero time duration T of the interaction between the observed system and the microscopic…
In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics (QM). We will argue that --leaving aside instrumentalism which restricts the physical…
Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
The measuring process is an external intervention in the dynamics of a quantum system. It involves a unitary interaction of that system with a measuring apparatus, a further interaction of both with an unknown environment causing…
Stochastic systems consisting of a very large number of independent elementary processes of the same kind, especially the radioactive decay, are considered as quantum clocks. By adapting the framework of the previously introduced concept of…
We address how one can empirically infer properties of quantum states generated by dynamics involving measurements. Our focus is on many-body settings where the number of measurements is extensive, making brute-force approaches based on…
Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…
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…
A symbolic analysis of observed time series data requires making a discrete partition of a continuous state space containing observations of the dynamics. A particular kind of partition, called ``generating'', preserves all dynamical…
This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…
We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…