Asymptotic Entanglement Research Articles

Quantum Information Spreading in Generalized Dual-Unitary Circuits.

We study the spreading of quantum information in a recently introduced family of brickwork quantum circuits that generalizes the dual-unitary class. These circuits are unitary in time, while their spatial dynamics is unitary only in a restricted subspace. First, we show that local operators spread at the speed of light as in dual-unitary circuits, i.e., the butterfly velocity takes the maximal value allowed by the geometry of the circuit. Then, we prove that the entanglement spreading can still be characterized exactly for a family of compatible initial states (in fact, for an extension of the compatible family of dual-unitary circuits) and that the asymptotic entanglement slope is again independent on the Rényi index. Remarkably, however, we find that the entanglement velocity is generically smaller than 1. We use these properties to find a closed-form expression for the entanglement-membrane line tension.

Quantum flux operators for Carrollian diffeomorphism in general dimensions

We construct Carrollian scalar field theories in general dimensions, mainly focusing on the boundaries of Minkowski and Rindler spacetime, whose quantum flux operators form a faithful representation of Carrollian diffeomorphism up to a central charge, respectively. At future/past null infinity, the fluxes are physically observable and encode rich information of the radiation. The central charge may be regularized to be finite by the spectral zeta function or heat kernel method on the unit sphere. For the theory at the Rindler horizon, the effective central charge is proportional to the area of the bifurcation surface after regularization. Moreover, the zero mode of supertranslation is identified as the modular Hamiltonian, linking Carrollian diffeomorphism to quantum information theory. Our results may hold for general null hypersurfaces and provide new insight in the study of the Carrollian field theory, asymptotic symmetry group and entanglement entropy.

Entanglement dynamics with string measurement operators

We explain how to apply a Gaussian-preserving operator to a fermionic Gaussian state. We use this method to study the evolution of the entanglement entropy of an Ising spin chain undergoing a quantum-jump dynamics with string measurement operators. We find that, for finite-range string operators, the asymptotic entanglement entropy exhibits a crossover from a logarithmic to an area-law scaling with the system size, depending on the Hamiltonian parameters as well as on the measurement strength. For ranges of the string which scale extensively with the system size, the asymptotic entanglement entropy shows a volume-law scaling, independently of the measurement strength and the Hamiltonian dynamics. The same behavior is observed for the measurement-only dynamics, suggesting that measurements may play a leading role in this context.

Computable lower bounds on the entanglement cost of quantum channels

A class of lower bounds for the entanglement cost of any quantum state was recently introduced in Lami and Regula (2023 Nature Physics) in the form of entanglement monotones known as the tempered robustness and tempered negativity. Here we extend their definitions to point-to-point quantum channels, establishing a lower bound for the asymptotic entanglement cost of any channel, whether finite or infinite dimensional. This leads, in particular, to a bound that is computable as a semidefinite program and that can outperform previously known lower bounds, including ones based on quantum relative entropy. In the course of our proof we establish a useful link between the robustness of entanglement of quantum states and quantum channels, which requires several technical developments such as showing the lower semicontinuity of the robustness of entanglement of a channel in the weak*-operator topology on bounded linear maps between spaces of trace class operators.

Integrable quenches in the Hubbard model

We study the quench dynamics of the one-dimensional Hubbard model through the quench action formalism. We introduce a class of integrable initial states—expressed as product states over two sites—for which we can provide an exact characterisation of the late-time regime. This is achieved by finding a closed-form expression for the overlaps between our states and the Bethe ansatz eigenstates, which we check explicitly in the limits of low densities and infinite repulsion. Our solution gives access to the stationary values attained by local observables (we show the explicit example of the density of doubly occupied sites) and the asymptotic entanglement dynamics directly in the thermodynamic limit. Interestingly, we find that for intermediate interaction strength Rényi entropies display a double-slope structure.

Measuring postquench entanglement entropy through density correlations

Following a sudden change of interactions in an integrable system of one-dimensional fermions, we analyze the dependence of the static structure factor on the observation time after the quantum quench. At small waiting times after the quench, we map the system to noninteracting bosons such that we are able to extract their occupation numbers from the Fourier transform of the density-density correlation function, and use these to compute a bosonic entropy from a diagonal ensemble. By comparing this bosonic entropy with the asymptotic steady-state entanglement entropy per fermion computed with exact diagonalization, we find excellent agreement.Received 8 December 2021Revised 17 March 2022Accepted 22 March 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L022023Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBosonizationCharge density wavesEntanglement entropyQuantum quenchTechniquesExact diagonalizationLuttinger liquid modelCondensed Matter, Materials & Applied PhysicsQuantum InformationStatistical Physics

Entanglement generation in(1+1)DQED scattering processes

We study real-time meson-meson scattering processes in $(1+1)$-dimensional QED by means of Tensor Networks. We prepare initial meson wave packets with given momentum and position introducing an approximation based on the free fermions model. Then, we compute the dynamics of two initially separated colliding mesons, observing a rich phenomenology as the interaction strength and the initial states are varied in the weak and intermediate coupling regimes. Finally, we consider elastic collisions and measure some scattering amplitudes as well as the entanglement generated by the process. Remarkably, we identify two different regimes for the asymptotic entanglement between the outgoing mesons: it is perturbatively small below a threshold coupling, past which its growth as a function of the coupling abruptly accelerates.

Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom

We study random quantum circuits and their rate of producing bipartite entanglement, specifically with respect to the choice of 2-qubit gates and the order (protocol) in which these are applied. The problem is mapped to a Markovian process and proved that there are large spectral equivalence classes -- different configurations have the same spectrum. Optimal gates and the protocol that generate entanglement with the fastest theoretically possible rate are identified. Relaxation towards the asymptotic thermal entanglement proceeds via a series of phase transitions in the local relaxation rate, which is a consequence of non-Hermiticity. In particular, non-Hermiticity can cause the rate to be either faster, or, even more interestingly, slower than predicted by the matrix eigenvalue gap. This is caused by an exponential in system size explosion of expansion coefficient sizes resulting in a 'phantom' eigenvalue, and is due to non-orthogonality of non-Hermitian eigenvectors. We numerically demonstrate that the phenomenon occurs also in random circuits with non-optimal generic gates, random U(4) gates, and also without spatial or temporal randomness, suggesting that it could be of wide importance also in other non-Hermitian settings, including correlations.

Entanglement of a bipartite channel

The most general quantum object that can be shared between two distant parties is a bipartite channel, as it is the basic element to construct all quantum circuits. In general, bipartite channels can produce entangled states, and can be used to simulate quantum operations that are not local. While much effort over the last two decades has been devoted to the study of entanglement of bipartite states, very little is known about the entanglement of bipartite channels. In this work, we rigorously study the entanglement of bipartite channels as a resource theory of quantum processes. We present an infinite and complete family of measures of dynamical entanglement, which gives necessary and sufficient conditions for convertibility under local operations and classical communication. Then we focus on the dynamical resource theory where free operations are positive partial transpose (PPT) superchannels, but we do not assume that they are realized by PPT pre- and post-processing. This leads to a greater mathematical simplicity that allows us to express all resource protocols and the relevant resource measures in terms of semi-definite programs. Along the way, we generalize the negativity from states to channels, and introduce the max-logarithmic negativity, which has an operational interpretation as the exact asymptotic entanglement cost of a bipartite channel. Finally, we use the non-positive partial transpose (NPT) resource theory to derive a no-go result: it is impossible to distill entanglement out of bipartite PPT channels under any sets of free superchannels that can be used in entanglement theory. This allows us to generalize one of the long-standing open problems in quantum information - the NPT bound entanglement problem - from bipartite states to bipartite channels. It further leads us to the discovery of bound entangled POVMs.

Asymptotic Entanglement Sudden Death in Two Atoms with Dipole-Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning.

We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole–dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole–dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.

Dynamical Entanglement.

Unlike the entanglement of quantum states, very little is known about the entanglement of bipartite channels, called dynamical entanglement. Here we work with the partial transpose of a superchannel, and use it to define computable measures of dynamical entanglement, such as the negativity. We show that a version of it, the max-logarithmic negativity, represents the exact asymptotic dynamical entanglement cost. We discover a family of dynamical entanglement measures that provide necessary and sufficient conditions for bipartite channel simulation under local operations and classical communication and under operations with positive partial transpose.

Environmentally Induced Entanglement – Anomalous Behavior in the Adiabatic Regime

Considering two non-interacting qubits in the context of open quantum systems, it is well known that their common environment may act as an entangling agent. In a perturbative regime the influence of the environment on the system dynamics can effectively be described by a unitary and a dissipative contribution. For the two-spin Boson model with (sub-) Ohmic spectral density considered here, the particular unitary contribution (Lamb shift) easily explains the buildup of entanglement between the two qubits. Furthermore it has been argued that in the adiabatic limit, adding the so-called counterterm to the microscopic model compensates the unitary influence of the environment and, thus, inhibits the generation of entanglement. Investigating this assertion is one of the main objectives of the work presented here. Using the hierarchy of pure states (HOPS) method to numerically calculate the exact reduced dynamics, we find and explain that the degree of inhibition crucially depends on the parameter s determining the low frequency power law behavior of the spectral density J(ω)∼ωse−ω/ωc. Remarkably, we find that for resonant qubits, even in the adiabatic regime (arbitrarily large ωc), the entanglement dynamics is still influenced by an environmentally induced Hamiltonian interaction. Further, we study the model in detail and present the exact entanglement dynamics for a wide range of coupling strengths, distinguish between resonant and detuned qubits, as well as Ohmic and deep sub-Ohmic environments. Notably, we find that in all cases the asymptotic entanglement does not vanish and conjecture a linear relation between the coupling strength and the asymptotic entanglement measured by means of concurrence. Further we discuss the suitability of various perturbative master equations for obtaining approximate entanglement dynamics.

Rates of Multipartite Entanglement Transformations.

The theory of the asymptotic manipulation of pure bipartite quantum systems can be considered completely understood: the rates at which bipartite entangled states can be asymptotically transformed into each other are fully determined by a single number each, the respective entanglement entropy. In the multipartite setting, similar questions of the optimally achievable rates of transforming one pure state into another are notoriously open. This seems particularly unfortunate in the light of the revived interest in such questions due to the perspective of experimentally realizing multipartite quantum networks. In this Letter, we report substantial progress by deriving simple upper and lower bounds on the rates that can be achieved in asymptotic multipartite entanglement transformations. These bounds are based on ideas of entanglement combing and state merging. We identify cases where the bounds coincide and hence provide the exact rates. As an example, we bound rates at which resource states for the cryptographic scheme of quantum secret sharing can be distilled from arbitrary pure tripartite quantum states. This result provides further scope for quantum internet applications, supplying tools to study the implementation of multipartite protocols over quantum networks.

Asymptotic states of accelerated qubits in nonzero background temperature

The study of the Unruh effect naturally raises the interest for a deeper understanding of the analogy between temperature and acceleration. A recurring question is whether an accelerated frame can be distinguished from an inertial thermal bath in pure thermodynamic experiments, such problem has been approached in the literature and a consensus is yet to be fully reached. In the present work we use the open quantum system formalism to investigate the case where both acceleration and background temperature are present. We find the asymptotic state density and entanglement generation from the Markovian evolution of accelerated qubits interacting with a thermal state of the external scalar field. Our results suggest that there is a very small asymmetry on the effects of the Unruh and background temperatures. Addressing the nonzero background temperature case is of both theoretical and phenomenological interest, thus the authors hope to enrich the existing discussions on the topic.

Asymptotic reduced density matrix of discrete-time quantum walks

In this article we show that for any quantum walker with m-dimensional coin subspace, we have m2 × m2 specific constant matrix where it completely determines the asymptotic reduced density matrix of the walker. We show that for any initial state with P0 projector, the reduced density matrix can be obtained by or equivalently . It is worth mentioning that the characteristic matrix is independent of the initial state and just depends on the coin operator, so by finding this matrix for a specific type of quantum walks (QW), the long-time behavior of it, such as local state of the coin after a long-time walk and asymptotic entanglement between the coin and position will be completely known for any initial state. We have found the characteristic matrix for the general coin operator, , as well as the exact form of this matrix for the local initial state.

Dynamics of relaxation and dressing of a quenched Bose polaron

We study the non-equilibrium dynamics of relaxation and dressing of a mobile impurity suddenly immersed--or quenched-- into a zero temperature homogeneous Bose Einstein condensate (BEC) with velocity $v$. A many body generalization of Weisskopf-Wigner theory is implemented to obtain the impurity fidelity, reduced density matrix and entanglement entropy. The dynamics depend crucially on the Mach number $\beta =v/c$, with $c$ the speed of sound of superfluid phonons and features many different time scales. Quantum Zeno behavior at early time is followed by relaxational and dressing dynamics determined by Cerenkov emission of long-wavelength phonons for $\beta >1$ with a decay rate $\Gamma_p \propto (\beta-1)^3$. The polaron dressing dynamics \emph{slows-down} as $\beta \rightarrow 1$ and is characterized by power laws $t^{-\alpha}$ with different exponents for $\beta \lessgtr 1$. The asymptotic entanglement entropy features a sharp discontinuity and the residue features a cusp at $\beta =1$. These non-equilibrium features suggest \emph{universal} dynamical critical phenomena near $\beta \simeq 1$, and are a direct consequence of the linear dispersion relation of long wavelength superfluid phonons. We conjecture on the emergence of an asymptotic dynamical attractor with $\beta \leq 1$.

The Asymptotic Spectrum of LOCC Transformations

We study the exact, non-deterministic conversion of multipartite pure quantum states into one-another via local operations and classical communication (LOCC) and asymptotic entanglement transformation under such channels. In particular, we consider the maximal number of copies of any given target state that can be extracted exactly from many copies of any given initial state as a function of the exponential decay in the success probability, known as the converse error exponent. We give a formula for the optimal rate presented as an infimum over the asymptotic spectrum of LOCC conversion. A full understanding of exact asymptotic extraction rates between pure states in the converse regime thus depends on a full understanding of this spectrum. We present a characterization of spectral points and use it to describe the spectrum in the bipartite case. This leads to a full description of the spectrum and thus an explicit formula for the asymptotic extraction rate between pure bipartite states, given a converse error exponent. This extends the result on entanglement concentration in [1] , where the target state is fixed as the Bell state. In the limit of vanishing converse error exponent, the rate formula provides an upper bound on the exact asymptotic extraction rate between two states, when the probability of success goes to 1. In the bipartite case, we prove that this bound holds with equality.

Ergodicity variation in a long range interacting one-dimensional Ising spin system subject to a time-varying magnetic field

We consider one dimensional Ising spin system in a transverse uniform time-dependent magnetic field. The asymptotic behavior of the bipartite entanglements between the terminal spin and each one of the other spins along the chain is investigated and compared at different spin-spin interaction ranges, from nearest neighbor to infinite long range, under the separate action of two different magnetic fields, constant and time-varying. We find that each of the nearest neighbor and next to nearest neighbor bipartite entanglements reach an asymptotic final state that is independent of the initial condition or the variation in the interaction range showing perfect ergodic behavior at quite short interaction ranges. However, the nearest neighbor entanglement maintains this behavior at a slightly longer ranges. The other bipartite entanglements assume a zero value within these interaction ranges. At intermediate short and long interaction ranges, the asymptotic states of all entanglements become strongly dependent on the initial state and the interaction range, deviating from the ergodic behavior observed before. The maximum asymptotic entanglement attainable between a pair of spins takes place at a long interaction range value that increases with the distance between the spins. At the infinite long range interaction, the dynamics of all bipartite entanglements coincide. great care should be taken in constructing both.

Connecting velocity and entanglement in quantum walks

We investigate the relation between transport properties and entanglement between the internal (spin) and external (position) degrees of freedom in one-dimensional discrete time quantum walks. We obtain closed-form expressions for the long-time position variance and asymptotic entanglement of quantum walks whose time evolution is given by any balanced quantum coin, starting from any initial qubit and position states following $\delta$-like (local) and Gaussian distributions. We find out that the knowledge of the limit velocity of the walker together with the polar angle of the initial qubit provide the asymptotic entanglement for local states, while this velocity with the quantum coin phases give it for highly delocalized states.

Spacetime Continuity and Quantum Information Loss

Continuity across the shock wave of two regions in the metric during the formation of a black hole can be relaxed in order to achieve information preservation. A Planck scale sized spacetime discontinuity leads to unitarity (a constant asymptotic entanglement entropy) by restricting the origin of coordinates (moving mirror) to be timelike. Moreover, thermal equilibration occurs and total evaporation energy emitted is finite.