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arXiv:quant-ph/0408152 · Physical Review A

Quantum-state transfer via the ferromagnetic chain in a spatially modulated field

Tao Shi, Ying Li, Z. Song, Chang-Pu Sun

Published Mar 11, 2005• 168 citations
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Abstract

We show that a perfect quantum-state transmission can be realized through a spin chain possessing the commensurate structure of an energy spectrum, which is matched with the corresponding parity. As an exposition of the mirror inversion symmetry discovered by Albanese et al. (e-print quant-ph∕0405029), the parity matched commensurability of the energy spectra helps us to present preengineered spin systems for quantum information transmission. Based on these theoretical analyses, we propose a protocol of near-perfect quantum-state transfer by using a ferromagnetic Heisenberg chain with uniform coupling constant, but an external parabolic magnetic field. The numerical results show that the initial Gaussian wave packet in this system with optimal field distribution can be reshaped near perfectly over a longer distance.

DOI
10.1103/physreva.71.032309

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We show that a perfect quantum-state transmission can be realized through a spin chain possessing the commensurate structure of an energy spectrum, which is matched with the corresponding parity. As an exposition of the mirror inversion symmetry discovered by Albanese et al. (e-print quant-ph∕0405029), the parity matched commensurability of the energy spectra helps us to present preengineered spin systems for quantum information transmission. Based on these theoretical analyses, we propose a protocol of near-perfect quantum-state transfer by using a ferromagnetic Heisenberg chain with uniform coupling constant, but an external parabolic magnetic field. The numerical results show that the initial Gaussian wave packet in this system with optimal field distribution can be reshaped near perfectly over a longer distance.
The quantum state transmission (QST) through the medium of high-dimensional many-particle system is studied with a symmetry analysis. We discover that, if the spectrum matches the symmetry of a fermion or boson system in a certain fashion, a perfect quantum state transfer can be implemented without any operation on the medium. Based on this observation the well-established results for the QST via quantum spin chains can be generalized to the high-dimensional many-particle systems with pre-engineered nearest neighbor (NN) hopping constants. By investigating a simple but realistic near half-filled tight-binding fermion system with uniform NN hopping integral, we show that an arbitrary many-particle state near the fermi surface can be perfectly transferred to its translational counterpart.
We propose a mechanism for perfect entanglement transport in anti-ferromagnetic (AFM) quantum spin chain systems with modulated exchange coupling and also for the modulation of on-site magnetic field. We use the principle of adiabatic quantum pumping process for entanglement transfer in the spin chain systems. We achieve the perfect entanglement transfer over an arbitrarily long distance and a better entanglement transport for longer AFM spin chain system than for the ferromagnetic one. We explain analytically and physically—why the entanglement hops in alternate sites. We find the condition for blocking of entanglement transport even in the perfect pumping situation. Our analytical solution interconnects quantum many body physics and quantum information science.
The quantum state transmission through the medium of high-dimensional many-particle system (boson or spinless fermion) is generally studied with a symmetry analysis. We discover that, if the spectrum of a Hamiltonian matches the symmetry of a fermion or boson system in a certain fashion, a perfect quantum state transfer can be implemented without any operation on the medium with pre-engineered nearest neighbor (NN). We also study a simple but realistic near half-filled tight-binding fermion system with uniform NN hopping integral. We show that an arbitrary many-particle state near the fermi surface can be perfectly transferred to its translational counterpart.
We propose to use ferromagnetic systems for entanglement generation and distribution together with perfect state transfer between distant parties in a qubit chain. The scheme relies on an effective two-qubit dynamics, realized by leaving two empty sites in a uniformly filled chain. This allows long-range interacting qubit chains to serve as quantum channels for both tasks with optimal performances. Remarkably, the entanglement between sender and receiver sites is independent of both the transmission distance and the system size. This property opens new perspectives for short- and mid-range quantum communication with qubit chains.
Perfect state transfer is possible in modulated spin chains [Phys. Rev. Lett. 92, 187902 (2004)], imperfections, however, are likely to corrupt the state transfer. We study the robustness of this quantum communication protocol in the presence of disorder both in the exchange couplings between the spins and in the local magnetic field. The degradation of the fidelity can be suitably expressed, as a function of the level of imperfection and the length of the chain, in a scaling form. In addition the time signal of fidelity becomes fractal. We further characterize the state transfer by analyzing the spectral properties of the Hamiltonian of the spin chain.