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arXiv:0910.1829 · Physical Review A

High-fidelity state transfer over an unmodulated linear XY spin chain

C. Allen Bishop, Yong-Cheng Ou, Zhao-Ming Wang, Mark Byrd

Published Apr 19, 2010• 20 citations
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Abstract

We provide a class of initial encodings that can be sent with a high fidelity over an unmodulated, linear, $\mathit{XY}$ spin chain. As an example, an average fidelity of $96%$ 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.

DOI
10.1103/physreva.81.042313

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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.
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 study transfer of a quantum state through XXXXXX spin chains with static imperfections. We combine the two standard approaches for state transfer based on (i) modulated couplings between neighboring spins throughout the spin chain and (ii) weak coupling of the outermost spins to an unmodulated spin chain. The combined approach allows us to design spin chains with modulated couplings and localized boundary states, permitting high-fidelity state transfer in the presence of random static imperfections of the couplings. The modulated couplings are explicitly obtained from an exact algorithm using the close relation between tridiagonal matrices and orthogonal polynomials [Linear Algebr. Appl. 21, 245 (1978)]. The implemented algorithm and a graphical user interface for constructing spin chains with boundary states (spinGUIn) are provided as Supplemental Material.
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 propose a scheme for using an unmodulated and unmeasured spin chain as a channel for short distance quantum communications. The state to be transmitted is placed on one spin of the chain and received later on a distant spin with some fidelity. We first obtain simple expressions for the fidelity of quantum state transfer and the amount of entanglement sharable between any two sites of an arbitrary Heisenberg ferromagnet using our scheme. We then apply this to the realizable case of an open ended chain with nearest neighbor interactions. The fidelity of quantum state transfer is obtained as an inverse discrete cosine transform and as a Bessel function series. We find that in a reasonable time, a qubit can be directly transmitted with better than classical fidelity across the full length of chains of up to 80 spins. Moreover, our channel allows distillable entanglement to be shared over arbitrary distances.