Transfer of arbitrary two qubit states via a spin chain

TL;DR

This paper derives a general formula for the fidelity of two-qubit quantum state transfer in arbitrary spin networks and demonstrates high-quality transfer in a 1D XX-Heisenberg chain with controlled local fields.

Contribution

It introduces a formalism linking two-qubit transfer fidelity to spin-excitation amplitudes and applies it to optimize transfer in a 1D spin chain.

Findings

High-fidelity two-qubit transfer is achievable with local field control.

Transfer time scales linearly or quadratically with chain length.

Almost perfect transfer is possible in a 1D XX-Heisenberg chain.

Abstract

We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-1/2 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 XX-Heisenberg type nearest-neighbour interactions adopting a protocol that is a generalization of the single qubit one proposed in Ref. [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.