Related papers: Generalized master equations leading to completely…
Stochastic resetting describes dynamics which are reinitialized to a reference state at random times. These protocols are attracting significant interest: they can stabilize nonequilibrium stationary states, generate correlations in…
A dynamical symmetry is employed to determine the structure of the quantum non-Markovian time-local master equation. Such a structure is composed from two components: scalar kinetic coefficients and the standard quantum Markovian operator…
Efficient methods for the description of the non-Markovian dynamics of open systems play an important role in many proposed applications of quantum mechanics. Here we review some of the most important tools that are based on the projection…
Understanding temporal processes and their correlations in time is of paramount importance for the development of near-term technologies that operate under realistic conditions. Capturing the complete multi-time statistics defining a…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
We propose to describe the dynamics of phase transitions in terms of a non-stationary Generalized Langevin Equation for the order parameter. By construction, this equation is non-local in time, i.e.~it involves memory effects whose…
The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of…
In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued…
A generalized exponential matrix based on the construction of kernel operators for generalized summability is defined and analyzing its main properties, generalizing the classical exponential matrix and fractional exponential matrix. This…
Featuring memory of past inputs is a fundamental requirement for machine learning models processing time-dependent data. In quantum reservoir computing, all architectures proposed so far rely on Markovian dynamics, which, as we prove,…
We propose a new form for the quantum master equation in the theory of open quantum systems. This new formalism allows one to describe the dynamics of two-level systems moving along different hyperbolic trajectories with distinct proper…
Understanding and simulating non-Markovian quantum dynamics remains an important challenge in open quantum system theory. A key advance in this endeavour would be to develop a unified mathematical description of non-Markovian dynamics, and…
Although the conditions for performing arbitrary unitary operations to simulate the dynamics of a closed quantum system are well understood, the same is not true of the more general class of quantum operations (also known as superoperators)…
Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with nonnegative entries. Based on this point of…
We study and compare the sensitivity of multiple non-Markovianity indicators for a qubit subjected to general phase-covariant noise. For each of the indicators, we derive analytical conditions to detect the dynamics as non-Markovian. We…
A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101 (R) (2005)]. For a single qubit…
The dynamics of an open quantum system can be described by a quantum operation, a linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to…
We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…
Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent…
A classical precursor to a full quantum dynamics for causal sets has been forumlated in terms of a stochastic sequential growth process in which the elements of the causal set arise in a sort of accretion process. The transition…