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We point to the connection between a recently introduced class of non-Markovian master equations and the general structure of quantum collisional models. The basic construction relies on three basic ingredients: a collection of time…
Existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to quantum simulations of time-independent quantum systems. We overcome this restriction to perturbative treatments with…
Time-dependent Lindblad master equations have important applications in areas ranging from quantum thermodynamics to dissipative quantum computing. In this paper we outline a general method for writing down exact solutions of time-dependent…
It is shown that if the decoherence matrix corresponding to a qubit master equation has a block-diagonal real part, then the evolution is determined by a one-dimensional oscillator equation. Further, when the full decoherence matrix is…
We are interested in the simulation of open quantum systems governed by the Lindblad master equation in an infinite-dimensional Hilbert space. To simulate the solution of this equation, the standard approach involves two sequential…
In this paper we consider a quantum open system and treat the master equation with some restricted dissipator which consists of a set of projection operators (projectors). The exact solution is given under the commutable approximation (in…
We introduce a variational hybrid classical-quantum algorithm to simulate the Lindblad master equation and its adjoint for time-evolving Markovian open quantum systems and quantum observables. Our method is based on a direct representation…
Open quantum systems provide an essential theoretical basis for the development of novel quantum technologies, since any real quantum system inevitably interacts with its environment. Lindblad master equations capture the effect of…
By splitting a Hamiltonian into two parts, using the solvability of eigenvalue problem of one part of the Hamiltonian, proving a useful identity and deducing an expansion formula of power of operator binomials, we obtain an explicit and…
We develop a Markovian master equation in the Lindblad form that enables the efficient study of a wide range of open quantum many-body systems that would be inaccessible with existing methods. The validity of the master equation is based…
Using the independent oscillator model with an arbitrary system potential, we derive a quantum Brownian equation assuming a correlated total initial state. Although not of Lindblad form, the equation preserves positivity of the density…
We treat several key stochastic equations for non-Markovian open quantum system dynamics and present a formalism for finding solutions to them via canonical perturbation theory, without making the Born-Markov or rotating wave approximations…
We derive an extremal equation for optimal completely-positive map which most closely approximates a given transformation between pure quantum states. Moreover, we also obtain an upper bound on the maximal mean fidelity that can be attained…
To understand typical dynamics of an open quantum system in continuous time, we introduce an ensemble of random Lindblad operators, which generate Markovian completely positive evolution in the space of density matrices. Spectral properties…
We present an algebraic framework for approximate model reduction of Markovian open quantum dynamics that guarantees complete positivity and trace preservation by construction. First, we show that projecting a Lindblad generator on its…
Master equations play a pivotal role in investigating open quantum systems. In particular, the Bloch-Redfield equation stands out due to its relation to a concrete physical environment. However, without further approximations it does not…
The majority of quantum open system models in the literature are simplistic in the sense that they only explicitly account for that part of the environment that directly interacts with the system of interest. A quantum open system with an…
The Lindblad equation is a widely used quantum master equation to model the dynamical evolution of open quantum systems whose states are described by density matrices. These solution matrices are characterized by semi-positiveness and trace…
We introduce a systematic approximation for an efficient evaluation of Born--Markov master equations for steady state transport studies in open quantum systems out of equilibrium: the energy resolved master equation approach. The master…
We consider a Lindblad equation that for particular initial conditions reduces to an asymmetric simple exclusion process with additional loss and gain terms. The resulting Lindbladian exhibits operator-space fragmentation and each block is…