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The master equation for the state of an open quantum system can be unravelled into stochastic trajectories described by a stochastic master equation. Such stochastic differential equations can be interpreted as an update formula for the…

We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps,…

Non-Markovian evolution of an open quantum system can be `unraveled' into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently we have…

Do stochastic Schr\"odinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system {\em on average} obeys a master equation, the answer is yes. Markovian stochastic Schr\"odinger…

It is well known that the state operator of an open quantum system can be generically represented as the solution of a time-local equation -- a quantum master equation. Unraveling in quantum trajectories offers a picture of open system…

We introduce jumptime unraveling as a distinct description of open quantum systems. As our starting point, we consider quantum jump trajectories, which emerge, physically, from continuous quantum measurements, or, formally, from the…

The cost of classical simulations of quantum many-body dynamics is often determined by the amount of entanglement in the system. In this paper, we study entanglement in stochastic quantum trajectory approaches that solve master equations…

By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose…

By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…

A large class of non-Markovian quantum processes in open systems can be formulated through time-local master equations which are not in Lindblad form. It is shown that such processes can be embedded in a Markovian dynamics which involves a…

The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the…

Quantum trajectories of a Markovian open quantum system arise from the back-action of measurements performed in the environment with which the system interacts. In this work, we consider counting measurements of quantum jumps, corresponding…

By using a condition of average trace preservation we derive a general class of non-Markovian Gaussian diffusive unravelings [L. Diosi and L. Ferialdi, Phys. Rev. Lett. \textbf{113}, 200403 (2014)], here valid for arbitrary non-Hermitian…

A central problem in the theory of the dynamics of open quantum systems is the derivation of a rigorous and computationally tractable master equation for the reduced system density matrix. Most generally, the evolution of an open quantum…

The fully quantized model of double qubits coupled to a common bath is solved using the quantum state diffusion (QSD) approach in the non-Markovian regime. We have established the explicit time-local non-Markovian QSD equations for the…

Every open-system dynamics can be associated to infinitely many stochastic pictures, called unravelings, which have proved to be extremely useful in several contexts, both from the conceptual and the practical point of view. Here, focusing…

Thirty years ago, the present author discussed pure state unraveling (stochastic quantum trajectories) of Markovian open system dynamics. The fact that he considered all positive dynamics, not restricted for the…

Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum trajectory'' techniques corresponding to continuous measurement schemes, which solve the master equation by…

We discuss the case of a Markovian master equation for an open system, as it is frequently found from environmental decoherence. We prove two theorems for the evolution of the quantum state. The first one states that for a generic initial…

The evolution of a quantum system undergoing repeated indirect measurements naturally leads to a Markov chain on the set of states which is called a quantum trajectory. In this paper we consider a specific model of such a quantum trajectory…