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arXiv:quant-ph/0604215 · Physical Review Letters

Long-Distance Entanglement in Spin Systems

Lorenzo Campos Venuti, C. Degli Esposti Boschi, M. Roncaglia

Published Jun 23, 2006• 169 citations
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Abstract

Most quantum system with short-ranged interactions show a fast decay of entanglement with the distance. In this Letter, we focus on the peculiarity of some systems to distribute entanglement between distant parties. Even in realistic models, like the spin-1 Heisenberg chain, sizable entanglement is present between arbitrarily distant particles. We show that long-distance entanglement appears for values of the microscopic parameters which do not coincide with known quantum critical points, hence signaling a transition detected only by genuine quantum correlations.

DOI
10.1103/physrevlett.96.247206

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Most quantum system with short-ranged interactions show a fast decay of entanglement with the distance. In this Letter, we focus on the peculiarity of some systems to distribute entanglement between distant parties. Even in realistic models, like the spin-1 Heisenberg chain, sizable entanglement is present between arbitrarily distant particles. We show that long-distance entanglement appears for values of the microscopic parameters which do not coincide with known quantum critical points, hence signaling a transition detected only by genuine quantum correlations.
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.
Entanglement, one of the most intriguing features of quantum theory and a main resource in quantum information science, is expected to play a crucial role also in the study of quantum phase transitions, where it is responsible for the appearance of long-range correlations. We investigate, through a microscopic calculation, the scaling properties of entanglement in spin chain systems, both near and at a quantum critical point. Our results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories. We explore some of the implications of this connection.
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.
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It is well known that the notions of spatial locality are often lost in quantum systems with long-range interactions, as exhibited by the emergence of phases with exotic long-range order and faster propagation of quantum correlations. We demonstrate here that such induced ``quasinonlocal'' effects do not necessarily translate to growth of global entanglement in the quantum system. By investigating the ground and quenched states of the variable-range, spin-1/2 Heisenberg Hamiltonian, we observe that the genuine multiparty entanglement in the system can either increase or counterintuitively diminish with a growing range of interactions. The behavior is reflective of the underlying phase structure of the quantum system and provides key insights for generation of multipartite entanglement in experimental atomic, molecular, and optical physics where such variable-range interactions have been implemented.