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Long distance entanglement in disordered spin chains

Jian Cui, Florian Mintert, Albert Ludwigs

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

We derive temporally shaped control pulses for the creation of long-distance entanglement in disordered spin chains. Our approach is based on a time-dependent target functional and a time-local control strategy that permits to ensure that the description of the chain in terms of matrix product states is always valid. With this approach, we demonstrate that long-distance entanglement can be created even for substantially disordered interaction landscapes.

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We derive temporally shaped control pulses for the creation of long-distance entanglement in disordered spin chains. Our approach is based on a time-dependent target functional and a time-local control strategy that permits to ensure that the description of the chain in terms of matrix product states is always valid. With this approach, we demonstrate that long-distance entanglement can be created even for substantially disordered interaction landscapes.
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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 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 investigate the emergence and properties of long-distance genuine multipartite entanglement, induced via three localized magnetic defects, in a one-dimensional transverse-field XXXXXX spin-1/21/21/2 chain. Using both analytical and numerical techniques, we determine the conditions for the existence of bound states localized at the defects. We find that the reduced density matrix (RDM) of the defects exhibits long-distance genuine multipartite entanglement (GME) across the whole range of the Hamiltonian parameter space, including regions where the two-qubit concurrence is zero. We quantify the entanglement by using numerical lower bounds for the GME concurrence, as well as by analytically deriving the GME concurrence in regions where the RDM is of rank 2. Our work provides insights into generating multipartite entanglement in many-body quantum systems via local control techniques.