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arXiv:1403.7833 · Physical Review A

Arbitrary perfect state transfer in d -level spin chains

Abolfazl Bayat

Published Jun 3, 2014• 37 citations
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Abstract

We exploit a ferromagnetic chain of interacting $d$-level ($d>2$) particles for arbitrary perfect transfer of quantum states with $(d\ensuremath{-}1)$ levels. The presence of one extra degree of freedom in the Hilbert space of particles, which is not used in encoding, allows one to achieve perfect transfer even in a uniform chain through a repeated measurement procedure with consecutive single site measurements. Apart from the first iteration, for which the time of evolution grows linearly with the size of the chain, in all other iterations, the evolution times are short and do not scale with the length. The success probability of the mechanism grows with the number of repetitions and practically after a few iterations the transfer is accomplished with a high probability.

DOI
10.1103/physreva.89.062302

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We suggest a protocol for the transfer of quantum information in spin chain channels with a finite recurrence time. By combining a dual-rail encoding with certain measurements at the receiving end, we can get arbitrarily perfect state transfer, i.e. by performing sufficiently many measurements at the receiving end, we can make the probability of perfect state transfer arbitrary close to unity. As an example of such an amplitude delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires in solid state quantum computers. Perfect state transfer with a probability of failure lower than delta in a Heisenberg chain of N spin-1/2 particles can be achieved in a timescale of the order of N^(7/3)*|ln(delta)|. Furthermore, the same scheme can be implemented using a single SU(n) chain which is realizable in quantum dot arrays.
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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.
The XX model with uniform couplings represents the most natural choice for quantum state transfer through spin chains. Given that it has long been established that single-qubit states cannot be transferred with perfect fidelity in this model, the notion of pretty good state transfer has been recently introduced as a relaxation of the constraints on fidelity. In this paper, we study the transfer of multi-qubit entangled and unentangled states through unmodulated spin chains, and we prove that it is possible to have pretty good state transfer of any multi-particle state. This significantly generalizes the previous results on single-qubit state transfer and opens the way to using uniformly coupled spin chains as short-distance quantum channels for the transfer of arbitrary states of any dimension. Our results could be tested with current technology.