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Long Distance Entanglement

Aires Ferreira, and J. M. B. Lopes dos Santos

Quantum Information and Condensed Matter physics inputs are required in the task of finding a reliable solution to quantum communication and computation based on a real solid state device. A reasonable amount of work has already been done in this particular topic.

Indeed, there is a current perspective of using the degrees of freedom of spin chain models (that describe the low-energy physics of several compounds and material) as qubits in order to establish quantum state transfer [1] or teleportation protocols [2]. 

We must be able to link several tiny quantum processing devices in order to achieve large-scale quantum computing. Very recently it was shown by numerical simulations that the ground state of several spin chains has the ability to entangle two spins very far apart without the need of external fields or of complicated measurements schemes [3]. This has strengthened the approach of using spin chains as quantum channels.

In a recent paper [4] we studied the physics of long distance entanglement (LDE) between two weakly interacting probes (e.g. spins) with general gapped strongly correlated systems. This was an important contribution in the sense it gave a theoretical framework to understand the mechanisms behind LDE and to show analytically its existence for a broad class of quantum systems. In particular,

-    we proved that an effective Hamiltonian describes the interaction of the probes mediated by a gapped many-body system. Moreover, we explicitly found the general expression of the effective couplings as function of the dynamical correlations of the bulk;

long distance entanglement 1

-    using the quantum field theory machinery, we showed that the finite antiferromagnetic Heisenberg spin-1/2 chain maximally entangles two spin-1/2 probes very far apart when a proper canonical transformation is made onto the spins in the bulk;

long distance entanglement 2

long distance entanglement 3

-    we showed for the first that the infinite biquadratic Heisenberg spin-1 model is able to produce LDE in the thermodynamic limit;

-    found an elegant interpretation of the origin of the effective couplings by means of linear response theory. More precisely, we found that the zero temperature DC response function of the system gives exactly the effective couplings.

long distance entanglement 4

These results constitute a significant step towards the understanding of the full capabilities of real solid state devices as quantum channels. Our work lead us to the conclusion that spin chains having dominant antiferromagnetic correlations will produce maximal LDE at temperatures smaller than the energy gap of such systems.

[1] S. Bose, Phys. Rev. Lett. 91, 207901 (2003).

[2] L. Campos Venuti, C. Degli Esposti Boschi, and M. Roncaglia, Phys. Rev. Lett. 99, 060401 (2007).

[3] L. Campos Venuti, C. Degli Esposti Boschi, and M. Roncaglia, Phys. Rev. Lett. 96, 247206 (2007).

[4] A. Ferreira and J. M. B. Lopes dos Santos, pre-print: arXiv.0708.0320

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