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Science Diliman

Effect of Spin Dimensionality in the Fidelity of Spin Chain Quantum Communication

Art Graeson Briones Dumigpe, Eric A. Galapon

Published Jun 16, 2017• 0 citations
OpenAlex

Abstract

We consider an unmodulated linear spin chain composed of two qubits at the ends, which undergo nearest-neighbor interactions, with an arbitrary spin between them. The state of the qubit on one end is to be transmitted through the arbitrary spin and is received by the qubit on the other end with some fidelity. We look at the behavior of the average f idelity of state transfer through time as affected by the spin quantum number of the arbitrary spin in between the qubits. We f ind that the higher the spin quantum number becomes, the earlier it takes to achieve perfect or nearly perfect state transfer. Moreover, when the channel with arbitrary spin is subjected to environment interaction, results from the calculation of average fidelity suggest that increasing the spin quantum number of the channel provides a countermeasure to the effects of decoherence induced by the environment.

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We consider the transfer of an arbitrary qubit state through a linear spin chain for N=4, 5, and 6 spins, each with a spin-S channel. We calculate the average fidelity between the arbitrary initial state of the qubit at one end and the time evolved qubit state at the opposite end of the chain. We show that increasing the quantum number S of the channel spins allows attaining near perfect state transfer at an earlier time for the isotropic exchange case. We also show that an opposite effect is observed in the anisotropic case.
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We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-12\frac{1}{2}21​ network, on a lattice of any dimensionality. Under the assumptions that the network Hamiltonian preserves the magnetization and that a fully polarized initial state is taken for the lattice, we obtain a general formula for the average fidelity of the two qubits QST, linking it to the one- and two-particle transfer amplitudes of the spin excitations among the sites of the lattice. We then apply this formalism to a 1D spin chain with XXXXXX-Heisenberg type nearest-neighbour interactions adopting a protocol that is a generalization of the single qubit one proposed in Paganelli et al. [Phys. Rev. A 87, 062309 (2013)]. We find that a high-quality two qubit QST can be achieved provided one can control the local fields at sites near the sender and receiver. Under such conditions, we obtain an almost perfect transfer in a time that scales either linearly or, depending on the spin number, quadratically with the length of the chain.
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