Entanglement Propagation Research Articles

Dynamical manifestation of the Gibbs paradox after a quantum quench

We study the propagation of entanglement after quantum quenches in the nonintegrable paramagnetic quantum Ising spin chain. Tuning the parameters of the system, we observe a sudden increase in the entanglement production rate, which we show to be related to the appearance of new quasiparticle excitations in the postquench spectrum. We argue that the phenomenon is the nonequilibrium version of the well-known Gibbs paradox related to mixing entropy and demonstrate that its characteristics fit the expectations derived from the quantum resolution of the paradox in systems with a nontrivial quasiparticle spectrum.

Entanglement contour perspective for “strong area-law violation” in a disordered long-range hopping model

We numerically investigate the link between the delocalization-localization transition and entanglement in a disordered long-range hopping model of spinless fermions by studying various static and dynamical quantities. This includes the inverse participation ratio, level-statistics, entanglement entropy and number fluctuations in the subsystem along with quench and wave-packet dynamics. Finite systems show delocalized, quasi-localized and localized phases. The delocalized phase shows strong area-law violation whereas the (quasi)localized phase adheres to (for large subsystems) the strict area law. The idea of `entanglement contour' nicely explains the violation of area-law and its relationship with `fluctuation contour' reveals a signature at the transition point. The relationship between entanglement entropy and number fluctuations in the subsystem also carries signatures for the transition in the model. Results from Aubry-Andre-Harper model are compared in this context. The propagation of charge and entanglement are contrasted by studying quench and wavepacket dynamics at the single-particle and many-particle levels.

Entanglement entropy with a time-dependent Hamiltonian

The time evolution of entanglement tracks how information propagates in interacting quantum systems. We study entanglement entropy in ${\mathrm{CFT}}_{2}$ with a time-dependent Hamiltonian. We perturb by operators with time-dependent source functions and use the replica trick to calculate higher-order corrections to entanglement entropy. At first order, we compute the correction due to a metric perturbation in ${\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}$ and find agreement on both sides of the duality. Past first order, we find evidence of a universal structure of entanglement propagation to all orders. The central feature is that interactions entangle unentangled excitations. Entanglement propagates according to ``entanglement diagrams,'' proposed structures that are motivated by accessory spacetime diagrams for real-time perturbation theory. To illustrate the mechanisms involved, we compute higher-order corrections to free fermion entanglement entropy. We identify an unentangled operator, one which does not change the entanglement entropy to any order. Then, we introduce an interaction and find it changes entanglement entropy by entangling the unentangled excitations. The entanglement propagates in line with our conjecture. We compute several entanglement diagrams. We provide tools to simplify the computation of loop entanglement diagrams, which probe UV effects in entanglement propagation in CFT and holography.

Thermalization after holographic bilocal quench

We study thermalization in the holographic (1 + 1)-dimensional CFT after simultaneous generation of two high-energy excitations in the antipodal points on the circle. The holographic picture of such quantum quench is the creation of BTZ black hole from a collision of two massless particles. We perform holographic computation of entanglement entropy and mutual information in the boundary theory and analyze their evolution with time. We show that equilibration of the entanglement in the regions which contained one of the initial excitations is generally similar to that in other holographic quench models, but with some important distinctions. We observe that entanglement propagates along a sharp effective light cone from the points of initial excitations on the boundary. The characteristics of entanglement propagation in the global quench models such as entanglement velocity and the light cone velocity also have a meaning in the bilocal quench scenario. We also observe the loss of memory about the initial state during the equilibration process. We find that the memory loss reflects on the time behavior of the entanglement similarly to the global quench case, and it is related to the universal linear growth of entanglement, which comes from the interior of the forming black hole. We also analyze general two-point correlation functions in the framework of the geodesic approximation, focusing on the study of the late time behavior.

Exact solution for the quench dynamics of a nested integrable system

Integrable models provide an exact description for a wide variety of physical phenomena. For example nested integrable systems contain different species of interacting particles with a rich phenomenology in their collective behavior, which is the origin of the unconventional phenomenon of spin-charge separation. So far, however, most of the theoretical work in the study of non-equilibrium dynamics of integrable systems has focussed on models with an elementary (i.e. not nested) Bethe ansatz. In this work we explicitly investigate quantum quenches in nested integrable systems, by generalizing the application of the quench action approach. Specifically, we consider the spin-1 Lai–Sutherland model, described, in the thermodynamic limit, by the theory of two different species of Bethe-ansatz particles, each one forming an infinite number of bound states. We focus on the situation where the quench dynamics starts from a simple matrix product state for which the overlaps with the eigenstates of the Hamiltonian are known. We fully characterize the post-quench steady state and perform several consistency checks for the validity of our results. Finally, we provide predictions for the propagation of entanglement and mutual information after the quench, which can be used as signature of the quasi-particle content of the model.

Comments on entanglement propagation

We extend our work on entanglement propagation following a local quench in 2+1 dimensional holographic conformal field theories. We find that entanglement propagates along an emergent lightcone, whose speed of propagation vE seems distinct from other measures of quantum information spreading. We compare the relations we find to information and hydrodynamic velocities in strongly coupled 2+1 dimensional theories. While early-time entanglement velocities corresponding to small entangling regions are numerically close to the butterfly velocity, late-time entanglement velocities for large regions show less regularity. We also generalize and extend our previous results regarding the late-time decay of the entanglement entropy back to its equilibrium value.

Scattering effect on entanglement propagation in RCFTs

In this paper we discuss the scattering effect on entanglement propagation in RCFTs. In our setup, we consider the time evolution of excited states created by the insertion of many local operators. Our results show that because of the finiteness of quantum dimension, entanglement is not changed after the scattering in RCFTs. In this mean, entanglement is conserved after the scattering event in RCFTs, which reflects the integrability of the system. Our results are also consistent with the free quasiparticle picture after the global quenches.

Generalized Dyson model: Nature of the zero mode and its implication in dynamics

We study the role of the anomalous $E=0$ state in dynamical properties of non-interacting fermionic chains with chiral symmetry and correlated bond disorder in one dimension. These models posses a diverging density of states at zero energy leading to a divergent localization length at the band center. By analytically calculating the localization length for a finite system, we show that correlations in the disorder modify the spatial decay of the $E = 0$ state from being quasilocalized to extended. We numerically simulate charge and entanglement propagation and provide evidence that states close to $E=0$ dominate the dynamical properties. Remarkably, we find that correlations lead to subdiffusive charge propagation, whereas the growth of entanglement is logarithmically slow. A logarithmic scaling of entanglement saturation with system size is also observed, which indicates a behavior akin to quantum critical glasses.

Spread of entanglement and causality

We investigate causality constraints on the time evolution of entanglement entropy after a global quench in relativistic theories. We first provide a general proof that the so-called tsunami velocity is bounded by the speed of light. We then generalize the free particle streaming model of arXiv:cond-mat/0503393 to general dimensions and to an arbitrary entanglement pattern of the initial state. In more than two spacetime dimensions the spread of entanglement in these models is highly sensitive to the initial entanglement pattern, but we are able to prove an upper bound on the normalized rate of growth of entanglement entropy, and hence the tsunami velocity. The bound is smaller than what one gets for quenches in holographic theories, which highlights the importance of interactions in the spread of entanglement in many-body systems. We propose an interacting model which we believe provides an upper bound on the spread of entanglement for interacting relativistic theories. In two spacetime dimensions with multiple intervals, this model and its variations are able to reproduce intricate results exhibited by holographic theories for a significant part of the parameter space. For higher dimensions, the model bounds the tsunami velocity at the speed of light. Finally, we construct a geometric model for entanglement propagation based on a tensor network construction for global quenches.

Creation of a low-entropy quantum gas of polar molecules in an optical lattice.

Ultracold polar molecules, with their long-range electric dipolar interactions, offer a unique platform for studying correlated quantum many-body phenomena. However, realizing a highly degenerate quantum gas of molecules with a low entropy per particle is challenging. We report the synthesis of a low-entropy quantum gas of potassium-rubidium molecules (KRb) in a three-dimensional optical lattice. We simultaneously load into the optical lattice a Mott insulator of bosonic Rb atoms and a single-band insulator of fermionic K atoms. Then, using magnetoassociation and optical state transfer, we efficiently produce ground-state molecules in the lattice at those sites that contain one Rb and one K atom. The achieved filling fraction of 25% should enable future studies of transport and entanglement propagation in a many-body system with long-range dipolar interactions.

Quasiparticle engineering and entanglement propagation in a quantum many-body system.

The key to explaining and controlling a range of quantum phenomena is to study how information propagates around many-body systems. Quantum dynamics can be described by particle-like carriers of information that emerge in the collective behaviour of the underlying system, the so-called quasiparticles. These elementary excitations are predicted to distribute quantum information in a fashion determined by the system's interactions. Here we report quasiparticle dynamics observed in a quantum many-body system of trapped atomic ions. First, we observe the entanglement distributed by quasiparticles as they trace out light-cone-like wavefronts. Second, using the ability to tune the interaction range in our system, we observe information propagation in an experimental regime where the effective-light-cone picture does not apply. Our results will enable experimental studies of a range of quantum phenomena, including transport, thermalization, localization and entanglement growth, and represent a first step towards a new quantum-optic regime of engineered quasiparticles with tunable nonlinear interactions.

Entanglement propagation and typicality of measurements in the quantum Kac ring

We study the time evolution of entanglement in a new quantum version of the Kac ring, where two spin chains become dynamically entangled by quantum gates, which are used instead of the classical markers. The features of the entanglement evolution are best understood by using knowledge about the behavior of an ensemble of classical Kac rings. For instance, the recurrence time of the quantum many-body system is twice the length of the chain and “thermalization” only occurs on time scales much smaller than the dimension of the Hilbert space. The model thus elucidates the relation between the results of measurements in quantum and classical systems: While in classical systems repeated measurements are performed over an ensemble of systems, the corresponding result is obtained by measuring the same quantum system prepared in an appropriate superposition repeatedly.

Local Properties of Entanglement and Application to Collapse

When a quantum system is macroscopic and becomes entangled with a microscopic one, this entanglement is not immediately total, but gradual and local. A study of this locality is the starting point of the present work and shows unexpected and detailed properties in the generation and propagation of entanglement between a measuring apparatus and a microscopic measured system. Of special importance is the propagation of entanglement in nonlinear waves with a finite velocity. When applied to the entanglement between a macroscopic system and its environment, this study yields also new results about the resulting disordered state. Finally, a mechanism of wave function collapse is proposed as an effect of perturbation in the growth of local entanglement between a measuring system and the measured one by waves of entanglement with the environment.

Unbounded Growth of Entanglement in Models of Many-Body Localization

An important and incompletely answered question is whether a closed quantum system of many interacting particles can be localized by disorder. The time evolution of simple (unentangled) initial states is studied numerically for a system of interacting spinless fermions in one dimension described by the random-field XXZ Hamiltonian. Interactions induce a dramatic change in the propagation of entanglement and a smaller change in the propagation of particles. For even weak interactions, when the system is thought to be in a many-body localized phase, entanglement shows neither localized nor diffusive behavior but grows without limit in an infinite system: interactions act as a singular perturbation on the localized state with no interactions. The significance for proposed atomic experiments is that local measurements will show a large but nonthermal entropy in the many-body localized state. This entropy develops slowly (approximately logarithmically) over a diverging time scale as in glassy systems.

Propagation of the interaction generating the macroscopic entanglement in a XX spin- $$\frac{1} {2}$$ chain with a staggered magnetic field

An effective Poynting vector associated to a XX chain of a spin-\(\frac{1} {2}\) with staggered magnetic field, B l = B + e −iπl b is derived. Such a field is not likely to occur in nature although the model is analytically solvable and allows to study macroscopic correlation (entanglement witnessing) [J. Hide, W. Son, I. Lawrie, V. Vedral, Phys. Rev. A 76, 022319 (2007)]. It is found that the propagation of the interaction generating of the macroscopic correlations has a component which is not along to the axis of the chain. This questions the idea that the propagation of the macroscopic (multipartite) entanglement takes place exclusively along the axis of the chain of XX spin-\(\frac{1} {2}\). We point out that in general, that the propagation of macroscopic entanglement is not an one-dimensional phenomenon but this occurs in a region of the space. Some reliable criteria for macroscopic correlation in terms of our effective Poynting’s vector are derived. Associated with entanglement propagation, an effective group velocity by volume unit that satisfies a Lieb-Robinson-like upper bound for the velocity of the propagation of the information has been found.

Entanglement transfer via XXZ Heisenberg chain with DM interaction

The role of spin-orbit interaction, arises from the Dzyaloshinski-Moriya anisotropic antisymmetric interaction, on the entanglement transfer via an antiferromagnetic XXZ Heisenberg chain is investigated. From symmetrical point of view, the XXZ Hamiltonian with Dzyaloshinski-Moriya interaction can be replaced by a modified XXZ Hamiltonian which is defined by a new exchange coupling constant and rotated Pauli operators. The modified coupling constant and the angle of rotations are depend on the strength of Dzyaloshinski-Moriya interaction. In this paper we study the dynamical behavior of the entanglement propagation through a system which is consist of a pair of maximally entangled spins coupled to one end of the chain. The calculations are performed for the ground state and the thermal state of the chain, separately. In both cases the presence of this anisotropic interaction make our channel more efficient, such that the speed of transmission and the amount of the entanglement are improved as this interaction is switched on. We show that for large values of the strength of this interaction a large family of XXZ chains becomes efficient quantum channels, for whole values of an isotropy parameter in the region $-2 \leq \Delta \leq 2$.

Generation and propagation of entanglement in driven coupled-qubit systems

In a bipartite system subject to decoherence from two separate reservoirs, entanglement is typically destroyed faster than where there is a single reservoir. Surprisingly, however, the existence of separate reservoirs can also have a beneficial entangling effect: if the qubits are coupled and driven externally by a classical field, the system ends in a stationary state characterized by a finite degree of entanglement. This phenomenon occurs only in a certain region of the parameter space and the structure of the stationary state has a universal form which does not depend on the initial state or on the specific physical realization of the qubits. We show that the entanglement thus generated can be propagated within a quantum network using simple local unitary operations. We suggest the use of such systems as ‘batteries of entanglement’ in quantum circuits.

Control, measurement, and propagation of entanglement in photon pairs generated through type-II parametric down-conversion

We present a study of the effects of dispersion on the properties of photon pairs generated by type-II collinear spontaneous parametric down-conversion. Specifically, we take into consideration the effects of a chirped pump, as well as of dispersive propagation of the photon pairs. We present expressions for the joint amplitude both in the spectral and temporal domains, as well as for the chronocyclic Wigner function of heralded single photons, which fully characterizes the single-photon spectral (temporal) properties. On the one hand, we show that unwanted effects of pump chirp in terms of the heralded single-photon duration can be suppressed for states designed to be factorable and spectrally elongated. On the other hand, we show that pump chirp constitutes an effective tool for the control of the degree of photon-pair entanglement. We show that when frequency-entangled photon pairs propagate through a dispersive medium, entanglement can ``migrate'' between the modulus and phase of the joint temporal amplitude.

Entanglement propagation through spin chains in the presence of a staggered magnetic field

We study the dynamics of entanglement in an $XY$ spin chain subject to a staggered magnetic field and contrast it to the previously discussed uniform field case. We find that in the isotropic $(XX)$ limit a staggered field can provide almost equally favorable conditions for a high-fidelity transfer of entanglement, while even a modest amount of exchange anisotropy appears to have a strong detrimental effect. We also study interactions between different waves of entanglement and assess the possibility of simultaneous transmission of multiple bits of quantum information.

Entanglement propagation through spin chains in the presence of a staggered magnetic field

Entanglement propagation through spin chains in the presence of a staggered magnetic field