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Scientific Reports

Engineering of entanglement and spin state transfer via quantum chains of atomic spins at large separations

Д. И. Бажанов, Ilia N. Sivkov, V. S. Stepanyuk

Published Sep 14, 2018• 19 citations
Publisher

Abstract

Several recent experiments have shown that long-range exchange interactions can determine collective magnetic ground states of nanostructures in bulk and on surfaces. The ability to generate and control entanglement in a system with long-range interaction will be of great importance for future quantum technology. An important step forward to reach this goal is the creation of entangled states for spins of distant magnetic atoms. Herein, the generation of long-distance entanglement between remote spins at large separations in bulk and on surface is studied theoretically, based on a quantum spin Hamiltonian and time-dependent Schrödinger equation for experimentally realized conditions. We demonstrate that long-distance entanglement can be generated between remote spins by using an appropriate quantum spin chain (a quantum mediator), composed by sets of antiferromagnetically coupled spin dimers. Ground state properties and quantum spin dynamics of entangled atoms are studied. We demonstrate that one can increase or suppress entanglement by adding a single spin in the mediator. The obtained result is explained by monogamy property of entanglement distribution inside a quantum spin system. We present a novel approach for non-local sensing of remote magnetic adatoms via spin entanglement.

DOI
10.1038/s41598-018-32145-3

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Several recent experiments have shown that long-range exchange interactions can determine collective magnetic ground states of nanostructures in bulk and on surfaces. The ability to generate and control entanglement in a system with long-range interaction will be of great importance for future quantum technology. An important step forward to reach this goal is the creation of entangled states for spins of distant magnetic atoms. Herein, the generation of long-distance entanglement between remote spins at large separations in bulk and on surface is studied theoretically, based on a quantum spin Hamiltonian and time-dependent Schrödinger equation for experimentally realized conditions. We demonstrate that long-distance entanglement can be generated between remote spins by using an appropriate quantum spin chain (a quantum mediator), composed by sets of antiferromagnetically coupled spin dimers. Ground state properties and quantum spin dynamics of entangled atoms are studied. We demonstrate that one can increase or suppress entanglement by adding a single spin in the mediator. The obtained result is explained by monogamy property of entanglement distribution inside a quantum spin system. We present a novel approach for non-local sensing of remote magnetic adatoms via spin entanglement.
We study the ground-state entanglement in systems of spins forming the boundary of a quantum spin network in arbitrary geometries and dimensionality. We show that as long as they are weakly coupled to the bulk of the network, the surface spins are strongly entangled, even when distant and not directly interacting, thereby generalizing the phenomenon of long-distance entanglement occurring in quantum spin chains. Depending on the structure of the couplings between surface and bulk spins, we discuss in detail how the patterns of surface entanglement can range from multipair bipartite to fully multipartite. In the context of quantum information and communication, these results find immediate application to the implementation of quantum routers, that is, devices able to distribute quantum correlations on demand among multiple network nodes.
Recent numerical results showed that spin chains are able to produce long-distance entanglement (LDE). We develop a formalism that allows the computation of LDE for weakly interacting probes with gapped many-body systems. At zero temperature, a dc response function determines the ability of the physical system to generate genuine quantum correlations between the probes. We show that the biquadratic Heisenberg spin-1 chain is able to produce LDE in the thermodynamic limit and that the finite antiferromagnetic Heisenberg chain maximally entangles two spin-1/21/21/2 probes very far apart. These results support the current perspective of using quantum spin chains as entanglers or quantum channels in quantum information devices.
We propose two schemes to produce long-distance entanglement in a spin chain. The first is based on a controllable interaction system, one starts from an entangled kernel and adds weaken interaction spins to the boundary sites step by step, then the entanglement will be extended longer and longer and its value is equal to that of its kernel. The second is based on a uniform interaction (J) system with a bulk magnetic field (B) that is absent for the boundary qubits, as long as B|J > 5, one can obtain near perfect long distance entanglement. Ultra-low temperature is needed in both schemes.
We discuss the phenomenon of long-distance entanglement (LDE) in the ground state of quantum spin models, its use in high-fidelity and robust quantum communication, and its realization in many-body systems of ultracold atoms in optical lattices and in arrays of coupled optical cavities. We investigate XX quantum spin models on one-dimensional lattices with open ends and different patterns of site-dependent interaction couplings, singling out two general settings: patterns that allow for perfect LDE in the ground state of the system, namely such that the end-to-end entanglement remains finite in the thermodynamic limit, and patterns of quasi-long-distance entanglement (QLDE) in the ground state of the system, namely such that the end-to-end entanglement vanishes with a very slow power-law decay as the length of the spin chain is increased. We discuss physical realizations of these models in ensembles of ultracold bosonic atoms loaded in optical lattices. We show how, using either suitably engineered super-lattice structures or exploiting the presence of edge impurities in lattices with single periodicity, it is possible to realize models endowed with nonvanishing LDE or QLDE. We then study how to realize models that optimize the robustness of QLDE at finite temperature and in the presence of imperfections using suitably engineered arrays of coupled optical cavities. For both cases the numerical estimates of the end-to-end entanglement in the actual physical systems are thoroughly compared with the analytical results obtained for the spin model systems. We finally introduce LDE-based schemes of long-distance quantum teleportation in linear arrays of coupled cavities, and show that they allow for high-fidelity and high success rates even at moderately high temperatures.
In distributed quantum networks, interacting spin systems can mediate the generation of highly entangled links between distant nodes. We investigate the role of effective parity-time (PT)-symmetric non-Hermitian spin-1/2 bulks weakly coupled to two quantum links, obtained due to the environmental interactions affecting both the bulk and the links. Focusing on effective non-Hermitian nearest-neighbor (NN) Su-Schrieffer-Heeger (SSH) models, we analyze how non-Hermiticity influences the dynamical formation of long-distance entanglement (LDE). For a paradigmatic model consisting of a quantum XX bulk subjected to imaginary staggered magnetic fields, we analytically determine the exceptional points arising from the resulting bulk-mediated interactions between the links. Combining analytical and numerical methods, we demonstrate that an initially fully separable state can dynamically evolve into highly entangled link states near these exceptional points in the broken regime. Further, after optimizing over time and system parameters, near-unit time-averaged entanglement between the links emerges under weak imaginary magnetic fields and bulk-link couplings, which cannot be attained in the corresponding Hermitian systems. Moreover, the non-Hermitian dynamics exhibit a freezing of high entanglement in the vicinity of exceptional points, a feature absent in Hermitian counterparts. We also identify regimes of long-range interaction strengths that yield a higher time-averaged entanglement than the corresponding NN models. Furthermore, we establish that LDE persists in the stationary regime, highlighting the promise of engineered non-Hermitian dynamics for realizing robust and frozen entangled links in quantum networks.
We consider a system of multiple qubits without any quantum control. We show that one can mediate entanglement between different subsystems in a controlled way by adding a (locally) controlled auxiliary system of the same size that couples via an always-on, distant dependent interaction to the system qubits. Solely by changing the internal state of the control system, one can selectively couple it to selected qubits, and ultimately generate different kinds of entanglement within the system. This provides an alternative way for quantum control and quantum gates that does not rely on the ability to switch interactions on and off at will, and can serve as a locally controlled quantum switch where all entanglement patterns can be created. We demonstrate that such an approach also offers an increased error tolerance w.r.t. position fluctuations.