Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects

We give a pedagogical introduction to the generalized hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.

Phase analysis on the error scaling of entangled qubits in a 53-qubit system

We have studied carefully the behaviors of entangled qubits on the IBM Rochester with various connectivities and under a “noisy” environment. A phase trajectory analysis based on our measurements of the GHZ-like states is performed. Our results point to an important fact that entangled qubits are “protected” against environmental noise by a scaling property that impacts only the weighting of their amplitudes. The reproducibility of most measurements has been confirmed within a reasonably short gate operation time. But there still are a few combinations of qubits that show significant entanglement evolution in the form of transitions between quantum states. The phase trajectory of an entangled evolution, and the impact of the sudden death of GHZ-like states and the revival of newly excited states are analyzed in details. All observed trajectories of entangled qubits arise under the influences of the newly excited states in a “noisy” intermediate-scale quantum (NISQ) computer.

Phase Analysis on the Error Scaling of Entangled Qubits in a 53-Qubit System

We have studied carefully the behaviors of entangled qubits on the IBM Rochester with various connectivities and under a “noisy” environment. A phase trajectory analysis based on our measurements of the GHZ-like states is performed. Our results point to an important fact that entangled qubits are “protected” against environmental noise by a scaling property that impacts only the weighting of their amplitudes. The reproducibility of most measurements has been confirmed within a reasonably short gate operation time. But there still are a few combinations of qubits that show significant entanglement evolution in the form of transitions between quantum states. The phase trajectory of an entangled evolution, and the impact of the sudden death of GHZ-like states and the revival of newly excited states are analyzed in details. All observed trajectories of entangled qubits arise under the influences of the newly excited states in a “noisy” intermediate-scale quantum (NISQ) computer.

Unitarity of entanglement and islands in two-sided Janus black holes

We explore the entanglement evolution of boundary intervals in eternal Janus black holes that can be embedded consistently into string theory in the low-energy limit. By studying the geodesics we show that there is a transition in the entanglement characteristic around the Page time, which manifests the unitarity of the evolution. We reproduce and reinterpret these bulk results from two different lower-dimensional perspectives: first as an interface CFT in the usual AdS/CFT correspondence and second as an effective gravity theory in one lower dimension coupled to a radiation background. In the limit where the number of interface degrees of freedom becomes large, we obtain an effective theory on appropriate branes that replace the deep interior region in the bulk, coined the shadow region. In this effective theory, we also identify the island of the radiation entanglement wedge and verify the newly proposed quantum extremization method. Our model clarifies that double holography with gravity in two higher dimensions can be realized in a concrete and consistent way and that the occurrence of islands is natural in one higher dimension. Furthermore, our model reveals that there can be a transitional behavior of the Page curve before the Page time, which is related to the emergence of new matter degrees of freedom on the branes.

Dynamics of two qubits in common environment

We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso- and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then work out an analog of the Born–Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement (Entanglement Sudden Death) at finite moments and its revivals (Entanglement Sudden Birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.

Entanglement dynamics of two atoms coupling to a quantum cavity

Recently, strong coupling dominating dissipative and decoherence effects between the atom and a quantum cavity has been investigated experimentally. In this paper, we study the entanglement dynamics of two two-level atoms coupling to a quantum cavity where each mirror is formed by a chain of atoms trapped near a one-dimensional waveguide. We consider the effects of both Markovian dynamics and non-Markovian dynamics on the entanglement evolution of the two central atoms. Our results show that the steady entanglement can be generated between the two central atoms whether the system is under the Markov regime or non-Markov regime when the number of atoms of the atomic mirrors is finite. When the number of the atomic mirrors is large enough, the entanglement of two central atoms takes oscillating behavior without a stable value. The effect of detuning and dissipation on entanglement dynamics is also discussed and the results imply that the detuning plays an important role in improving the entanglement amplitude.

Entanglement evolution and generalised hydrodynamics: interacting integrable systems

We investigate the dynamics of bipartite entanglement after the sudden junction of two leads in interacting integrable models. By combining the quasiparticle picture for the entanglement spreading with Generalised Hydrodynamics we derive an analytical prediction for the dynamics of the entanglement entropy between a finite subsystem and the rest. We find that the entanglement rate between the two leads depends only on the physics at the interface and differs from the rate of exchange of thermodynamic entropy. This contrasts with the behaviour in free or homogeneous interacting integrable systems, where the two rates coincide.