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Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes…
We propose a new approach concerning the introduction of time-irreversibility in statistical mechanics. It is based on a transition function defined in terms of path integral and verifying a time-irreversible equation. We show first how…
Time dependent quantum systems have become indispensable in science and its applications, particularly at the atomic and molecular levels. Here, we discuss the approximation of closed time dependent quantum systems on bounded domains, via…
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time ). The…
A quantum measurement can be described by a set of matrices, one for each possible outcome, which represents the positive operator-valued measure (POVM) of the sensor. Efficient protocols of POVM extraction for arbitrary sensors are…
At present, several models for quantum computation have been proposed. Adiabatic quantum computation scheme particularly offers this possibility and is based on a slow enough time evolution of the system, where no transitions take place. In…
We address the statistics of a simultaneous CWLM of two non-commuting variables on a few-state quantum system subject to a conditioned evolution. Both conditioned quantum measurement and that of two non-commuting variables differ…
In this paper we propose a new state observer design technique for nonlinear systems. It consists of an extension of the recently introduced parameter estimation-based observer, which is applicable for systems verifying a particular…
In this study, we address the challenge of controlling quantum systems under environmental influences using the theory of dynamical invariants. We employ a reverse engineering approach to develop control protocols designed to be robust…
The model of open quantum systems is adopted to describe the non-local dynamical behaviour of qubits processed by entangling gates. The analysis gets to the conclusion that a distinction between evaluation steps and task-oriented computing…
We present a basic introduction to the dynamics of open quantum systems based on local-in-time master equations. We characterize the properties of time-local generators giving rise to legitimate completely positive trace preserving quantum…
Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of…
We develop techniques to analyse the statistics of completion times of non-deterministic elements in quantum entanglement generation, and how they affect the overall performance as measured by the secret key rate. By considering such…
We describe quantum tomography as an inverse statistical problem and show how entropy methods can be used to study the behaviour of sieved maximum likelihood estimators. There remain many open problems, and a main purpose of the paper is to…
Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized…
We report an approach to quantum open system dynamics that leads to novel nonlinear constant relations governing information flow among the participants. Our treatment is for mixed state systems entangled in a pure state fashion with an…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…
Quantum machine learning is a rapidly advancing discipline that leverages the features of quantum mechanics to enhance the performance of computational tasks. Quantum reservoir processing, which allows efficient optimization of a single…