Related papers: Markovian Marignals
We give an explicit entropy production formula for a class of quantum Markov semigroups, arising in the weak coupling limit of a system coupled with reservoirs, whose generators $\mathcal{L}$ are sums of other generators…
We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we proof a pivotal convergence theorem for finite Markov chains and a minimal version of the…
We provide a solution to the problem of determining whether a target pure state can be asymptotically prepared using dissipative Markovian dynamics under fixed locality constraints. Beside recovering existing results for a large class of…
Expanding upon the rich history of algebraic techniques in probability, we show the existence of and construct a Markov chain using the Hopf square map on a quantum group that is both non-commutative and non-cocommutative. This extends the…
The existence of global-in-time bounded martingale solutions to a general class of cross-diffusion systems with multiplicative Stratonovich noise is proved. The equations describe multicomponent systems from physics or biology with…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…
We develop a martingale theory to describe fluctuations of entropy production for open quantum systems in nonequilbrium steady states. Using the formalism of quantum jump trajectories, we identify a decomposition of entropy production into…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable…
We present a construction of genuinely entangled multipartite quantum states based on the group theory. Analyzed states resemble the Dicke states, whereas the interactions occur only between specific subsystems related by the action of the…
We postulate the existence of universal crossover functions connecting the universal parts of the entanglement entropy to the low temperature thermal entropy in gapless quantum many-body systems. These scaling functions encode the intuition…
We investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints.…
For quantum phases of Hamiltonian ground states, the energy gap plays a central role in ensuring the stability of the phase as long as the gap remains finite. We propose Markov length, the length scale at which the quantum conditional…
Markovian master equations, often called Liouvillians or Lindbladians, are used to describe decay and decoherence of a quantum system induced by that system's environment. While a natural environment is detrimental to fragile quantum…
In this letter we investigate the possibility of observing macroscopic entanglement, considering realistic factors such as decoherence, particle losses, and measurements of limited precision (coarse-grained collective measurements). This…
We present a general framework that reveals substructures of genuine multipartite entanglement. Via simple inequalities it is possible to discriminate different sets of multipartite qubit states. These inequalities are beneficial regarding…