epl draft Entanglement generation between distant parties via disordered spin chains

We study the emergence of bipartite entanglement between a pair of spins weakly connected to the ends of a linear disordered XY spin-1/2 channel. We analyze how their concurrence responds to structural and on-site fluctuations embodied by long-range spatially-correlated sequences. We show that the end-to-end entanglement is very robust against disorder and asymmetries in the channel provided that the degree of correlations are strong enough and both entangling parties are tuned accordingly. Our results offer further alternatives in the design of stable quantum communication protocols via imperfect channels. Introduction. – Transmitting quantum states and establishing entanglement between different quantum processing units are essential ingredients towards the implementation of large-scale quantum computing [1]. In this context, a promising approach relies on using solid-state devices such as spin chains with pre-engineered interactions as quantum channels [2] for quantum communication protocols. In such, the information is usually encoded locally and after proper channel initialization and subsequent time evolution, the initial state (say, a qubit) can be retrieved at the desired location, or entanglement can be created during the process. The key point is to devise the protocols whose working principle is based solely upon how chain is engineered, avoiding the need of external control as much as possible. After the overall concept was put forward by Bose in Ref. [2], much effort has been devoted to find out further schemes for performing quantum-state transfer (QST) [3–13] and entanglement creation/distribution protocols [14–19]. The versatility offered by spin chains comes with a price though. The lack of dynamical control implies that the manufacturing process of the chain must be very accurate. Otherwise, the appearance of imperfections (e.g. disorder) should compromise the desired output. There lies the importance of evaluating the robustness of such quantum communication protocols in the presence of noise [19–26]. In this letter, we go along that direction and address the influence of disorder in weakly-coupled spin models [5–7]. In the QST framework, a pair of spins are perturbatively connected to, say, each end of a XY spin-1/2 chain thereby spanning a decoupled Hamiltonian involving both spins only or added with a given normal mode of the channel once their frequency goes in resonance with it [6]. Ideally, that is, in a noiseless channel, this decoupling process yields the appearance of maximally entangled Bell-type eigenstates which are responsible for Rabilike oscillations between the sender and receiver spins thus allowing for high-fidelity QST performances [13]. Random fluctuations, on the other hand, will act on the channel by shuffling the spectrum, promoting localization, and thus destroying the mirror symmetry of every eigenstate of the system [24]. When correlated fluctuations – say, spatially dependent – are present the scenario is rather different. For instance, it was shown that short-range correlations in the disorder distribution promotes the breakdown of Anderson localization in 1D models [27]. The effect of long-range correlations is even more dramatic as it induces a metal-insulator transition with sharp mobility edges [28, 29]. The coexistence between localized and delocalized states hence provides a rich set of dynamical regimes to explore [29–31]. For example, it has been reported [19] that the emergence of correlated fluctuations in the local magnetic fields is capable of enhance the distribution of entanglement in XY spin chains. Here we investigate how long-range correlated diagonal (local magnetic fields) and off-diagonal (spin couplings) p-1 ar X iv :1 71 1. 08 55 3v 1 [ qu an tph ] 2 3 N ov 2 01 7 G. M. A. Almeida1 F. A. B. F. de Moura1 M. L. Lyra1 disorder affect the stability of the entanglement developed between two distant spins, both being perturbatively coupled to the disordered channel. We consider fluctuations which follow a power-law spectrum of the form S(k) ∝ 1/k, with k being the corresponding wave number and α is an exponent that characterizes the degree of those correlations with α = 0 standing for the uncorrelated case. For high-enough values of α we find that the end-to-end concurrence reaches about its maximum value despite the fact that significant amounts of disorder are still present. We further discuss what kind of profile a given channel must have in order to mediate entanglement in the presence of imperfections. The emergence of a set of delocalized states in the middle of the spectrum when α > 2 [28] becomes crucial in generating an effective resonant coupling between both distant parties. Our findings settle a resilient framework for carrying out long-distance quantum communication protocols through highly disordered quantum channels. Model Hamiltonian. – Thorough the paper we consider a one-dimensional isotropic XY spin-1/2 chain with open boundaries featuring N + 2 spins labelled by i = 0, 1, 2, . , N,N + 1, with spins 0 and N + 1 denoting the parties aimed to get entangled. The full Hamiltonian of the system reads (h̄ = 1)