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

Abstract

We show that a perfect quantum state transmission can be realized through a spin chain possessing a commensurate structure of energy spectrum, which is matched with the corresponding parity. As an exposition of the mirror inversion symmetry discovered by Albanese et. al (quant-ph/0405029), the parity matched the commensurability of energy spectra help us to present the novel pre-engineered spin systems for quantum information transmission. Based on the these theoretical analysis, 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 shows that the initial Gaussian wave packet in this system with optimal field distribution can be reshaped near-perfectly over a longer distance.

Quantum spin chains with fractional revival

“…Hahn [18,19,20], q-Krawtchouk [21] and q-Racah [10]. Of particular interest for what follows are models connected to the so-called para-Krawtchouk polynomials [13].…”

“…Note that the Krawtchouk chain parameters are recovered when θ = 0 and that contrary to the isospectral models with fractional revival covered in the last section, here, all the J ℓ are modified in comparison with those of (3.19). Interestingly, the para-Krawtchouk models have been shown in [13] to enact PST for 18) where M 1 and M 2 are positive co-prime integers and M 1 is odd. Let us here explain how spin chains that lead to fractional revival can also exhibit perfect state transfer.…”

Perfect state transfer: Beyond nearest-neighbor couplings

“…Choosing which lattice sites to place the spins on is a discretized form of the problem, and is not covered in this formalism. The best that we can achieve is to allow some additional engineering, such as local magnetic fields, and tune these to give the closest match to a particular spectrum [6]. We could envisage a variety of such systems in which we do not have control over a sufficient number of parameters.…”

“…This wire would be a chain of qubits, with a fixed interaction, capable of transferring a quantum state from one end of the chain to the other. Following the initial investigation of wires [1], and subsequent demonstration that perfect quantum wires exist [2,3], a large number of papers have been published about optimising the schemes over a variety of parameters such as the robustness against errors, or a restricted ability to engineer the state (see, for example, [4,5,6,7]). Novel modifications of such chains have also been presented for the generation of entangled states or the application of unitary operations during the transfer [8].…”

Noise effects in perfect transmission of quantum states

“…This idea was first introduced in [1], where it was shown that the natural dynamics of a Heisenberg ferromagnetic spin chain can achieve high-fidelity transfer of qubits over distances as long as 80 lattice units.In contrast to this traditional "passive" protocol, different approaches soon emerged. One idea was to engineer the couplings between the various spins in the chain in such a way that states are transferred with perfect [2]- [9] or with arbitrary high fidelity [10]- [16]; in addition, some minimal external control on the chain dynamics was also introduced in order to achieve similar results [18]- [26].…”