Related papers: A classification of open Gaussian dynamics
The required set of operations for universal continuous-variable quantum computation can be divided into two primary categories: Gaussian and non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed as a sequence of…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…
Classical gravitational evolution admits an elegant and compact re-expression in terms of gauge covariant generalizations of Lie derivatives with respect to a spatial phase space dependent $su(2)$ valued vector field called the Electric…
Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is…
We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for non-Markovian damped harmonic oscillator. In the general framework, the results demonstrate the possibility to use a closed system as a simulator…
We consider the transport of electrons passing through a mesoscopic device possessing internal dynamical quantum degrees of freedom. The mutual interaction between the system and the conduction electrons contributes to the current…
Completely positive quantum operations are frequently discussed in the contexts of statistical mechanics and quantum information. They are customarily given by maps forming positive operator-values measures. To intuitively understand…
We present control schemes for open quantum systems that combine decoupling and universal control methods with coding procedures. By exploiting a general algebraic approach, we show how appropriate encodings of quantum states result in…
We show how quantum dynamics can be captured in the state of a quantum system, in such a way that the system can be used to stochastically perform, at a later time, the stored transformation perfectly on some other quantum system. Thus…
Non-Markovian master equations describe general open quantum systems when no approximation is made. We provide the exact closed master equation for the class of Gaussian, completely positive, trace preserving, non-Markovian dynamics. This…
An open stochastic system \`a la Jan Willems is a system affected by two qualitatively different kinds of uncertainty: one is probabilistic fluctuation, and the other one is nondeterminism caused by a fundamental lack of information. We…
The reduced dynamics of an open quantum system $S$, interacting with its environment $E$, is not completely positive, in general. In this paper, we demonstrate that if the two following conditions are satisfied, simultaneously, then the…
The abstract mathematical structure behind the positive energy quantization of linear classical systems is described. It is separated into 3 stages: the description of a classical system, the algebraic quantization and the Hilbert space…
A relativistic quantum mechanics is studied for bound hadronic systems in the framework of the Point Form Relativistic Hamiltonian Dynamics. Negative energy states are introduced taking into account the restrictions imposed by a correct…
We consider a class of open quantum many-body systems that evolves in a Markovian fashion, the dynamical generator being in GKS-Lindblad form. Here, the Hamiltonian contribution is characterized by an all-to-all coupling, and the…
Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the unitary system…
In this lecture we present a brief outline of boson Fock space stochastic calculus based on the creation, conservation and annihilation operators of free field theory, as given in the 1984 paper of Hudson and Parthasarathy. We show how a…
The stochastic generators of Markov-regular operator cocycles on symmetric Fock space are studied in a variety of cases: positive cocycles, projection cocycles, and partially isometric cocycles. Moreover a class of transformations of…
Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. However, in many approximated non-Markovian master equations, the positivity of the reduced density matrix is not…
We consider a closed quantum system subject to a stochastic resetting process. The generic expression for the resulting density operator is formulated for arbitrary resetting dynamics, fully characterised by the distribution of times…