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arXiv:1312.0360 · Physical Review A

Optimized quantum state transfer through an XY spin chain

Yang Liu, Dong Zhou

Published Jun 26, 2014• 11 citations
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Abstract

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 $XY$ 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.

DOI
10.1103/physreva.89.062331

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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.
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.
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.
The transfer of quantum states between distant nodes is one of the most fundamental tasks in quantum-information processing. Recent studies show that the antiferromagnetic spin chain initially prepared in a multi-excitation state can provide suitable pathways for quantum state transfer. In this paper, we investigate the quality of state transfer through a uniformly coupled antiferromagnetic spin chain where the initial state of the channel varies with the number of spin excitations. Firstly, by analyzing the dynamics of observables for the output qubit using the information-flux approach, the explicit relation about how the average fidelity of state transfer depends on the initial state of the spin channel is obtained. The results show that the average fidelity of state transfer through a multi-excitation spin channel only relates to the parity of the number of spin excitations in the channel. Then we compare the maximum average fidelity of state transfer through the odd-excitation with those through the even-excitation spin channels, and provide a simple criterion to optimize the quality of state transfer by choosing appropriate channels from the odd-excitation and the even-excitation channels. Compared with the previous studies which initialize the chains into the ground state of the ferromagnetic medium or the Nel state, the maximum average fidelity of state transfer is evidently enhanced by using the optimized channel. Moreover, we analyze the entanglement distribution through the channel having different number of spin excitations via the information-flux approach. It is found that the quality of entanglement distribution not only relates to the number of initial spin excitations present in the channel, but also depends on the initial ordering of these excited spins. The numerical results suggest that the amount of distributed entanglement and duration of distribution in the channel where all spins are down or up are larger than those in other excited channels. Based on these results, we can choose appropriate quantum channels for state transfer and entanglement distribution in practice.
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.
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.