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arXiv:0812.4578 · Physical Review A

Robust and reliable transfer of a qubit state through an XY spin chain

Zhao-Ming Wang, C. Allen Bishop, Mark Byrd, Bin Shao, Jian Zou

Published Aug 24, 2009• 26 citations
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Abstract

We present several protocols for reliable quantum state transfer through an XY spin chain. Among these is a simple two-spin encoding that achieves a remarkably high-fidelity transfer for an arbitrary quantum state. The fidelity of the transfer also decreases slowly with increasing chain length. Furthermore, the reliability can be increased by taking advantage of a local memory and/or confirming transfer using a second spin chain. The simplicity and high fidelity of the encoding makes this a candidate for near-future experiments including a test of the quantum speed limit.

DOI
10.1103/physreva.80.022330

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We present several protocols for reliable quantum state transfer through an XY spin chain. Among these is a simple two-spin encoding that achieves a remarkably high-fidelity transfer for an arbitrary quantum state. The fidelity of the transfer also decreases slowly with increasing chain length. Furthermore, the reliability can be increased by taking advantage of a local memory and/or confirming transfer using a second spin chain. The simplicity and high fidelity of the encoding makes this a candidate for near-future experiments including a test of the quantum speed limit.
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.
We provide a class of initial encodings that can be sent with a high fidelity over an unmodulated, linear, XY\mathit{XY}XY spin chain. As an example, an average fidelity of 9696%96 can be obtained using an 11-spin encoding to transmit a state over a chain containing 10 000 spins. An analysis of the magnetic-field dependence is given, and conditions for field optimization are provided.
Quantum state transfer along a one-dimensional spin chain has become a fundamental ingredient for quantum communication between distant nodes in a quantum network. We study the average fidelity of quantum state transfer (QST) along an XYXYXY spin chain by adjusting the basis identification between the first spin and the last spin. In a proper choice of the basis identification, we find that the QST fidelity depends only on the average parity of the initial state linearly. We propose a simple scheme to adjust the basis identification to optimize the average fidelity such that it depends linearly on the absolute value of the average parity. In the case where the absolute value of the average parity is 1 we prove that the fidelity takes the maximum at any time over arbitrary initial state and basis identification.
In this paper, we investigate a high-dimensional quantum state transfer protocol. An arbitrary unknown high-dimensional state can be transferred with high fidelity between two remote registers through an XXXXXX coupling spin chain of arbitrary length. The evolution of the state transfer is determined by the natural dynamics of the chain without external modulation and coupling strength engineering. As a consequence, entanglement distribution with a high efficiency can be achieved. Also the strong field and high spin quantum number can partly counteract the effect of finite temperature to ensure the high fidelity of the protocol when the quantum data bus is in the thermal equilibrium state under an external magnetic field.
A uniformly coupled double-quantum Hamiltonian for a spin chain has recently been implemented experimentally. We propose a method for the determination of initial quantum states that will provide perfect or near-perfect state transmission for an arbitrary Hamiltonian including this one. By calculating the eigenvalues and eigenvectors of a unitary operator obtained from the free evolution plus an exchange operator, we find that the double-quantum Hamiltonian spin chain will support a three-spin initial encoding that will transfer along the chain with remarkably high fidelity. The fidelity is also found to decrease very slowly with increasing chain length. In addition, we are able to explain previous results showing exceptional transfer using this method.