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arXiv:1210.7245 · Physical Review A

Long-distance entanglement generation by local rotational protocols in spin chains

Morteza Rafiee, Hossein Mokhtari

Published Feb 6, 2013• 6 citations
arXivHTMLPDF

Abstract

We exploit the inherent entanglement of the ground state of a spin chain with dimerized $XX$ and $XXZ$ Hamiltonians to investigate the entanglement generation between the ends of the chain. The strategy introduced by S. Yang, A. Bayat, and S. Bose [Phys. Rev. A 84, 020302(R) (2011)] is followed to encode the information in the entangled ground state of the system by local rotation. The amount of achieved entanglement in this scheme is higher than the one achieved when attaching a pair of maximally entangled spins to the system. Also, our proposal can be implemented by using the optical lattices.

DOI
10.1103/physreva.87.022304

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We exploit the inherent entanglement of the ground state of a spin chain with dimerized XXXXXX and XXZXXZXXZ Hamiltonians to investigate the entanglement generation between the ends of the chain. The strategy introduced by S. Yang, A. Bayat, and S. Bose [Phys. Rev. A 84, 020302(R) (2011)] is followed to encode the information in the entangled ground state of the system by local rotation. The amount of achieved entanglement in this scheme is higher than the one achieved when attaching a pair of maximally entangled spins to the system. Also, our proposal can be implemented by using the optical lattices.
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We present a protocol for quantum state transfer and remote state preparation across spin chains which operate in their antiferromagnetic mode. The proposed mechanism harnesses the inherent entanglement of the ground state of the strongly correlated many-body systems which naturally exists for free. The uniform Hamiltonian of the system does not need any engineering and, during the whole process, remains intact while a single-qubit measurement followed by a single-qubit rotation are employed for both encoding and inducing dynamics in the system. This, in fact, has been inspired by recent progress in observing spin waves in optical lattice experiments, in which manipulation of the Hamiltonian is hard and instead local rotations and measurements have become viable. The attainable average fidelity stays above the classical threshold for chains up to length 50 and the system shows very good robustness against various sources of imperfection.
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.
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We show that the inherent entanglement of the ground state of strongly correlated systems can be exploited for both classical and quantum communications. Our strategy is based on a single-qubit rotation that encodes information in the entangled nature of the ground state. In classical communication, our mechanism conveys more than one bit of information in each shot, just as dense coding does, without demanding long-range entanglement. In our scheme for quantum communication, the quality is higher than the widely studied attaching scenarios. Moreover, we propose to implement this way of communication in optical lattices.
We suggest a method of entangling significantly the distant ends of a spin chain using minimal control. This entanglement between distant individual spins is brought about solely by exploiting the dynamics of an initial mixed state with N\'eel order if the lattice features nearest-neighbor XXZXXZXXZ interaction. There is no need to control single spins or to have engineered couplings or to pulse globally. The method only requires an initial nonadiabatic switch (a quench) between two Hamiltonians followed by an evolution under the second Hamiltonian. The scheme is robust to randomness of the couplings as well as the finiteness of an appropriate quench and could potentially be implemented in various experimental setups, ranging from atoms in optical lattices to Josephson-junction arrays.