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Advances in Mathematical Physics

Entanglement Transfer through an Antiferromagnetic Spin Chain

Abolfazl Bayat, Sougato Bose

Published Dec 27, 2009• 24 citations
Publisher

Abstract

We study the possibility of using an uniformly coupled finite antiferromagnetic spin‐1/2 Heisenberg chain as a channel for transmitting entanglement. One member of a pair of maximally entangled spins is initially appended to one end of a chain in its ground state and the dynamical propagation of this entanglement to the other end is calculated. We show that, compared to the analogous scheme with a ferromagnetic chain in its ground state, here the entanglement is transmitted faster, with less decay, with a much higher purity and as a narrow pulse form rising nonanalytically from zero. Here nonzero temperatures and depolarizing environments are both found to be less destructive in comparison to the ferromagnetic case. The entanglement is found to propagate through the chain in a peculiar fashion whereby it hops to skip alternate sites.

DOI
10.1155/2010/127182

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We study the possibility of using an uniformly coupled finite antiferromagnetic spin‐1/2 Heisenberg chain as a channel for transmitting entanglement. One member of a pair of maximally entangled spins is initially appended to one end of a chain in its ground state and the dynamical propagation of this entanglement to the other end is calculated. We show that, compared to the analogous scheme with a ferromagnetic chain in its ground state, here the entanglement is transmitted faster, with less decay, with a much higher purity and as a narrow pulse form rising nonanalytically from zero. Here nonzero temperatures and depolarizing environments are both found to be less destructive in comparison to the ferromagnetic case. The entanglement is found to propagate through the chain in a peculiar fashion whereby it hops to skip alternate sites.
We study the possibility of using an uniformly coupled finite antiferromagnetic spin-1/2 Heisenberg chain as a channel for transmitting entanglement. One member of a pair of maximally entangled spins is initially appended to one end of a chain in its ground state and the dynamical propagation of this entanglement to the other end is calculated. We show that compared to the analogous scheme with a ferromagnetic chain in its ground state, here the entanglement is transmitted faster, with less decay, with a much higher purity and as a narrow pulse form rising non-analytically from zero. Here non-zero temperatures and depolarizing environments are both found to be less destructive in comparison to the ferromagnetic case. The entanglement is found to propagate through the chain in a peculiar fashion whereby it hops to skip alternate sites.
We demonstrate how near-perfect entanglement (in fact arbitrarily close to maximal entanglement) can be generated between the end spins of an antiferromagnetic isotropic Heisenberg chain of length NNN, starting from the ground state in the N/2N/2N/2 excitation subspace, by applying a magnetic field along a given direction, acting on a single spin only. Temporally optimal magnetic fields to generate a singlet pair between the two end spins of the chain are calculated for chains up to length 202020 using optimal control theory. The optimal fields are shown to remain effective in various nonideal situations including thermal fluctuations, magnetic field leakage, random system couplings, and decoherence. Furthermore, the quality of the entanglement generated can be substantially improved by taking these imperfections into account in the optimization. In particular, the optimal pulse of a given thermal initial state is also optimal for any other initial thermal state with lower temperature.
We propose a scheme for using an unmodulated and unmeasured spin chain as a channel for short distance quantum communications. The state to be transmitted is placed on one spin of the chain and received later on a distant spin with some fidelity. We first obtain simple expressions for the fidelity of quantum state transfer and the amount of entanglement sharable between any two sites of an arbitrary Heisenberg ferromagnet using our scheme. We then apply this to the realizable case of an open ended chain with nearest neighbor interactions. The fidelity of quantum state transfer is obtained as an inverse discrete cosine transform and as a Bessel function series. We find that in a reasonable time, a qubit can be directly transmitted with better than classical fidelity across the full length of chains of up to 80 spins. Moreover, our channel allows distillable entanglement to be shared over arbitrary distances.
The zero-temperature pairwise entanglement is investigated in the antiferromagnetic Heisenberg chain with one impure spin s. The impurity location is varied from the open end to a mediate site of the spin chain. It is found that the pairwise entanglement is proportional to 1/s. This means that the entanglement will disappear in the classical systems as s → ∞. Compared to the isotropic Heisenberg chain without impurity, the efficient control of the spin coupling between the impurity spin and nearest-neighbor spins can enhance the pairwise entanglement.
We investigate the quality of quantum state transfer through a uniformly coupled antiferromagnetic spin chain in a multiexcitation subspace. The fidelity of state transfer using multiexcitation channels is found to compare well with communication protocols based on the ground state of a spin chain with ferromagnetic interactions. Our numerical results support the conjecture that the fidelity of state transfer through a multiexcitation subspace only depends on the number of initial excitations present in the chain and is independent of the excitation ordering. Based on these results, we describe a communication scheme which requires little effort for preparation.