We show that the entanglement evolution of an open quantum system is the same for the vast majority of initial pure states, in the limit of large Hilbert space dimensions. The analytical results are illustrated by a numerical study of the evolution of negativity for many-qubit systems undergoing a local decoherence process. In the limit of many subsystems, the arising mixed state entanglement between one subsystem and the rest grows more robust, whereas for two equally sized partitions it becomes more fragile.
The fact that in the course of an open evolution there is, in a vast majority of cases, the creation of system-environment entanglement out of the initial coherence, has been known for many years. However, how much entanglement can be created under general assumptions has not been analyzed yet. In this work, we investigate system-environment entanglement generation under a broad and important class of interactions known as pure dephasing interactions and for arbitrary initial conditions. Our main results are the following bounds on the relative entropy of entanglement
Er(σSE) after evolution: $ C_r(ρ_S) - H(\mathcal{I}|\mathcal{M}) \leq E_r(σ_{SE}) \leq C_r(ρ_S) - C_r(σ_S) + H(\mathcal{I})$, connecting it on one side to the initial relative entropy of coherence,
Cr(ρS), and information extractable from the environment,
H(I∣M), and on the other side to the decoherence strength, $ C_r(ρ_S) - C_r(σ_S)$, making quantitatively precise the statement that larger entanglement leads to more decoherence. As an illustration, we apply our results to the spin-boson model, where a qubit interacts with a bosonic bath, showing time evolution of the entanglement and the Markovian/non-Markovian crossover. Our results help better understand and quantify the complicated correlations, produced during an open evolution, which will hopefully lead to better and new decoherence mitigation techniques.
Interacting quantum systems evolving from an uncorrelated composite initial state generically develop quantum correlations---entanglement. As a consequence, a local description of interacting quantum systems is impossible as a rule. A unitarily evolving (isolated) quantum system generically develops extensive entanglement: the magnitude of the generated entanglement will increase without bounds with the effective Hilbert space dimension of the system. It is conceivable that coupling of the interacting subsystems to local dephasing environments will restrict the generation of entanglement to such extent that the evolving composite system may be considered as approximately disentangled. This conjecture is addressed in the context of some common models of a bipartite system with linear and nonlinear interactions and local coupling to dephasing environments. Analytical and numerical results obtained imply that the conjecture is generally false. Open dynamics of the quantum correlations is compared to the corresponding evolution of the classical correlations and a qualitative difference is found.
Conventional approaches to simulating quantum many-body dynamics produce a single trajectory: if the Hamiltonian or the initial state is changed, the computation must be re-performed. Recent efforts toward foundation models have begun to address this limitation, yet existing methods transfer across either Hamiltonians or initial states, but not both. In this work, we introduce the Universal Neural Propagator (UNP), a single, unified model that learns the functional mapping from driving protocols to time-evolution propagators. Trained in an entirely self-supervised way, a single UNP model predicts dynamics across a function space of driving protocols and an exponentially large Hilbert space of initial states simultaneously. We benchmark on a two-dimensional driven Ising model and demonstrate the UNP's accuracy and transferability across product and entangled initial states, as well as for both in- and out-of-distribution driving protocols. The UNP remains accurate at system sizes beyond exact diagonalization, and can be efficiently fine-tuned across all initial states using observable data. By shifting the object of learning from quantum states to operators, this work opens a route toward transferable simulation of driven quantum matter.
In the present thesis we investigate how the quantum entanglement of multicomponent systems evolves under realistic conditions. More specifically, we focus on open quantum systems coupled to the (uncontrolled) degrees of freedom of an environment. We identify key quantities that describe the entanglement dynamics, and provide efficient tools for its calculation. For quantum systems of high dimension, entanglement dynamics can be characterized with high precision. In the first part of this work, we derive evolution equations for entanglement. These formulas determine the entanglement after a given time in terms of a product of two distinct quantities: the initial amount of entanglement and a factor that merely contains the parameters that characterize the dynamics. The latter is given by the entanglement evolution of an initially maximally entangled state. A maximally entangled state thus benchmarks the dynamics, and hence allows for the immediate calculation or - under more general conditions - estimation of the change in entanglement. Thereafter, a statistical analysis supports that the derived (in-)equalities describe the entanglement dynamics of the majority of weakly mixed and thus experimentally highly relevant states with high precision. The second part of this work approaches entanglement dynamics from a topological perspective. This allows for a quantitative description with a minimum amount of assumptions about Hilbert space (sub-)structure and environment coupling. In particular, we investigate the limit of increasing system size and density of states, i.e. the macroscopic limit. In this limit, a universal behaviour of entanglement emerges following a "reference trajectory", similar to the central role of the entanglement dynamics of a maximally entangled state found in the first part of the present work.