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The transfer of excitations between different locations of a quantum many-body system is of primary importance in many research areas, from transport properties in spintronics and atomtronics to quantum state transfer in quantum information processing. We address the transfer of n > 1 bosonic and fermionic excitations between the edges of a one-dimensional chain modelled by a quadratic hopping Hamiltonian, where the block edges, embodying the sender and the receiver sites, are weakly coupled to the quantum wire. We find that perturbative high-quality transfer is attainable in the weak-coupling limit, for both bosons and fermions, only for certain modular arithmetic equivalence classes of the wire's length. Finally we apply our findings to the transport of spins and the charging of a many-body quantum battery., peer-reviewed

We investigate the transfer of genuine multipartite entanglement across a spin-1/2 chain with nearest-neighbor XX-type interaction. We focus on the perturbative regime, where a block of spins is weakly coupled at each edge of a quantum wire, embodying the role of a multiqubit sender and receiver, respectively. We find that high-quality multipartite entanglement transfer is achieved at the same time that three excitations are transferred to the opposite edge of the chain. Moreover, we find that both a finite concurrence and tripartite negativity is attained at much shorter time, making GHZ-distillation protocols feasible. Finally, we investigate the robustness of our protocol with respect to non-perturbative couplings and increasing lengths of the quantum wire., Comment: Comments welcome

In this work we study the single-qubit quantum state transfer in uniform long-range spin XXZ systems in high-dimensional geometries. We consider prototypical long-range spin exchanges that are relevant for experiments in cold atomic platforms: Coulomb, dipolar and van der Waals-like interactions. We find that in all these cases the fidelity increases with the dimensionality of the lattice. This can be related to the emergence of a pair of bilocalized states on the sender and receiver site due to the onset of an effective weak-coupling Hamiltonian. The enhancement of the quantum state transfer fidelity is more pronounced both with the increase of the couplings interaction range and in going from a 1D to a 2D lattice. Finally, we test our predictions in the presence of temperature-induced disorder introducing a model for the thermal displacement of the lattice sites, considered as a set of local adiabatic oscillators., 8 pages, 7 figures

Routing quantum information among different nodes in a network is a fundamental prerequisite for a quantum internet. While single-qubit routing has been largely addressed, many-qubit routing protocols have not been intensively investigated so far. Building on a recently proposed many-excitation transfer protocol, we apply the perturbative transfer scheme to a two-excitation routing protocol on a network where multiple two-receivers block are coupled to a linear chain. We address both the case of switchable and permanent couplings between the receivers and the chain. We find that the protocol allows for efficient two-excitation routing on a fermionic network, although for a spin-12 network only a limited region of the network is suitable for high-quality routing., ;, peer-reviewed

Generating high-quality multi-particle entanglement between communicating parties is the primary resource in quantum teleportation protocols. To this aim, we show that the natural dynamics of a single spin chain is able to sustain the generation of two pairs of Bell states - possibly shared between a sender and a distant receiver - which can in turn enable two-qubit teleportation. In particular, we address a spin-1/2 chain with XX interactions, connecting two pairs of spins located at its boundaries, playing the roles of sender and receiver. In the regime where both end pairs are weakly coupled to the spin chain, it is possible to generate at predefinite times a state that has vanishing infidelity with the product state of two Bell pairs, thereby providing nearly unit fidelity of teleportation. We also derive an effective Hamiltonian via a second-order perturbation approach that faithfully reproduces the dynamics of the full system., 11 pages, 4 figures. Comments welcome

We study the non-equilibrium evolution of a one-dimensional quantum Ising chain with spatially disordered, time-dependent, transverse fields characterised by white noise correlation dynamics. We establish pre-thermalization in this model, showing that the quench dynamics of the on-site transverse magnetisation first approaches a metastable state unaffected by noise fluctuations, and then relaxes exponentially fast towards an infinite temperature state as a result of the noise. We also consider energy transport in the model, starting from an inhomogeneous state with two domain walls which separate regions characterised by spins with opposite transverse magnetization. We observe at intermediate time scales a phenomenology akin to Anderson localization: energy remains localised within the two domain walls, until the Markovian noise destroys coherence and accordingly disorder-induced localization, allowing the system to relax towards the late stages of its non-equilibrium dynamics. We benchmark our results with the simpler case of a noisy quantum Ising chain without disorder, and we find that the pre-thermal plateau is a generic property of weakly noisy spin chains, while the phenomenon of pre-thermal Anderson localisation is a specific feature arising from the competition of noise and disorder in the real-time transport properties of the system., 6 pages, 3 figures

Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model's microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time $\tau_{bd}$, proportional to the size of the system. This behaviour is explained by noticing that the low-energy modes, responsible for the scaling properties, are resilient to the absorption of energy. Our results suggest that relevant features of the universality do hold also when the system is brought out-of-equilibrium by a periodic driving., Comment: 11 pages, 7 figures

We study the creation and distribution of entanglement in disordered $XY$-type spin-$1/2$ chains for the paradigmatic case of a single flipped spin prepared on a fully polarized background. The local magnetic field is set to follow a disordered long-range-correlated sequence with power-law spectrum. Depending on the degree of correlations of the disorder, a set of extended modes emerge in the middle of the band yielding an interplay between localization and delocalization. As a consequence, a rich variety of entanglement distribution patterns arises, which we evaluate here through the concurrence between two spins. We show that, even in the presence of disorder, the entanglement wave can be pushed to spread out reaching distant sites and also enhance pairwise entanglement between the initial site and the rest of the chain. We also study the propagation of an initial maximally-entangled state through the chain and show that correlated disorder improves the transmission quite significantly when compared with the uncorrelated counterpart. Our work contributes in designing solid-state devices for quantum information processing in the realistic setting of correlated static disorder., 11 pages, 7 figures

In this paper we discuss the implementation of 2-qubit quantum state transfer (QST) in inhomogeneous spin chains where the sender and the receiver blocks are coupled through the bulk channel via weak links. The fidelity and the typical timescale of the QST are discussed as a function of the parameters of the weak links. Given the possibility of implementing with cold atoms in optical lattices a variety of condensed matter systems, including spin systems, we also discuss the possible implementation of the discussed 2-qubit QST with cold gases with weak links, together with a discussion of the applications and limitations of the presented results.

We study finite size scaling for the magnetic observables of an impurity residing at the endpoint of an open quantum Ising chain in a transverse magnetic field, realized by locally rescaling the magnetic field by a factor $\mu \neq 1$. In the homogeneous chain limit at $\mu = 1$, we find the expected finite size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit, $\mu = 0$, we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. For this case, we provide both analytic approximate expressions for the magnetization and the susceptibility as well as numerical evidences for the scaling behavior. At intermediate values of $\mu$, finite size scaling is violated, and we provide a possible explanation of this result in terms of the appearance of a second, impurity related length scale. Finally, on going along the standard quantum-to-classical mapping between statistical models, we derive the classical counterpart of the quantum Ising chain with an impurity at its endpoint as a classical Ising model on a square lattice wrapped on a half-infinite cylinder, with the links along the first circle modified as a function of $\mu$.

We study the generation and propagation of local perturbations in a quantum many-body spin system. In particular, we study the Ising model in transverse field in the presence of a local field defect at one edge. This system possesses a rich phase diagram with different regions characterized by the presence of one or two Majorana zero modes. We show that their localized character {\it i}) enables a characterization of the Ising phase transition through a local-only measurement performed on the edge spin, and {\it ii}) strongly affects the propagation of quasiparticles emitted after the sudden removal of the defect, so that the dynamics of the local magnetization show clear deviations from a ballistic behavior in presence of the Majorana fermions., comments welcome

The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully predicts the equilibrium critical exponents for the crossover length and the order parameter of the model, and, moreover, implies a new exponent for the rescaled irreversible work. By connecting the irreversible work to the two-impurity spin correlation function, our findings can be tested experimentally., 6 pages, 4 figures

We numerically study the dynamics of entanglement entropy, induced by an oscillating time periodic driving of the transverse field, h(t), of a one-dimensional quantum Ising chain. We consider several realizations of h(t), and we find a number of results in analogy with entanglement entropy dynamics induced by a sudden quantum quench. After short-time relaxation, the dynamics of entanglement entropy synchronises with h(t), displaying an oscillatory behaviour at the frequency of the driving. Synchronisation in the dynamics of entanglement entropy, is spoiled by the appearance of quasi-revivals which fade out in the thermodynamic limit, and which we interpret using a quasi-particle picture adapted to periodic drivings. Taking the time-average of the entanglement entropy in the synchronised regime, we find that it obeys a volume law scaling with the subsystem's size. Such result is reminiscent of a thermal state or of a Generalised Gibbs ensemble of a quenched Ising chain, although the system does not heat up towards infinite temperature as a consequence of the integrability of the model., 6 pages, 3 figures

We consider a coupled-cavity array, where each cavity interacts with an atom under the rotating-wave approximation. For a staggered pattern of inter-cavity couplings, a pair of field normal modes each bi-localized at the two array ends arise. A rich structure of dynamical regimes can hence be addressed depending on which resonance condition between the atom and field modes is set. We show that this can be harnessed to carry out high-fidelity quantum-state transfer (QST) of photonic, atomic or polaritonic states. Moreover, by partitioning the array into coupled modules of smaller length, the QST time can be substantially shortened without significantly affecting the fidelity., 12 pages, 8 figures

The authors are indebted to T. S. Batalhao, J. Goold, R. Serra, and Peter Talkner for invaluable discussions., We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself., This work has been supported by a PERFEST grant (L. F.) from Universita degli Studi di Palermo, the Marie Curie Action, the UK EPSRC (EP/G004579/1 and EP/ L005026/1), the John Templeton Foundation (Grant ID 43467), the EU Collaborative Project TherMiQ (Grant Agreement No. 618074), and by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme through the project NeQuFlux Grant No. 623085 (M. C.). T. J. G. A. is supported by the European Commission, the European Social Fund, and the Region Calabria through the program POR Calabria FSE 2007-2013-Asse IV Capitale Umano-Obiettivo Operativo M2. A. X. acknowledges funding from the Royal Commission for the Exhibition of 1851. Part of this work was supported by the COST Action MP1209 “Thermodynamics in the Quantum Regime.”, peer-reviewed

We study the competing effects of simultaneous Markovian and non-Markovian decoherence mechanisms acting on a single spin. We show the existence of a threshold in the relative strength of such mechanisms above which the spin dynamics becomes fully Markovian, as revealed by the use of several non-Markovianity measures. We identify a measure-dependent nested structure of such thresholds, hinting at a causality relationship among the various non-Markovianity witnesses used in our analysis. Our considerations are then used to argue the unavoidably non-Markovian evolution of a single-electron quantum dot exposed to both intrinsic and Markovian technical noise, the latter of arbitrary strength.

Two different models for performing efficiently routing of a quantum state are presented. Both cases involve an XX spin chain working as data bus and additional spins that play the role of sender and receivers, one of which is selected to be the target of the quantum state transmission protocol via a coherent quantum coupling mechanism making use of local/global magnetic fields. Quantum routing is achieved, in the first of the models considered, by weakly coupling the sender and the receiver to the data bus. In the second model, strong magnetic fields acting on additional spins located between the sender/receiver and the data bus allow us to perform high fidelity routing., added references in v2

We study the transport of quantum correlations across a chain of interacting spin-1/2 particles. As a quantitative figure of merit, we choose a symmetric version of quantum discord and compare it with the transported entanglement, addressing various operating regimes of the spin medium. Discord turns out to be better transported for a wide range of working points and initial conditions of the system. We relate this behavior to the efficiency of propagation of a single excitation across the spin chain. Moreover, we point out the role played by a magnetic field in the dynamics of discord in the effective channel embodied by the chain. Our analysis can be interestingly extended to transport processes in more complex networks and the study of non-classical correlations under general quantum channels., 8 pages, 9 figures, RevTeX4

Using recently proposed measures for non-Markovianity [H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. {\bf 103}, 210401 (2009)], we study the dynamics of a qubit coupled to a spin environment via an energy-exchange mechanism. We show the existence of a point, in the parameter space of the system, where the qubit dynamics is effectively Markovian and that such a point separates two regions with completely different dynamical behaviors. Indeed, our study demonstrates that the qubit evolution can in principle be tuned from a perfectly forgetful one to a deep non-Markovian regime where the qubit is strongly affected by the dynamical back-action of the environmental spins. By means of quantum process tomography, we provide a complete and intuitive characterization of the qubit channel., 10 pages, 8 figures, RevTeX4

We study the dynamical behavior of two initially entangled qubits, each locally coupled to an environment embodied by an interacting spin chain. We consider energy-exchange qubit-environment couplings resulting in a rich and highly non trivial entanglement dynamics. We obtain exact results for the time-evolution of the concurrence between the two qubits and find that, by tuning the interaction parameters, one can freeze the dynamics of entanglement, therefore inhibiting its relaxation into the spin environments, as well as activate a sudden-death phenomenon. We also discuss the effects of an environmental quantum phase transition on the features of the two-qubit entanglement dynamics., 7 pages and a bit, 7 figures, RevTeX4