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International Conference on Quantum, Nano and Micro Technologies (ICQNM)

Spin-Chains as Quantum Channels for Qubit-State Transfer

Giulia Gualdi, Irene Marzoli, Paolo Tombesi

Published Feb 1, 2009• 0 citations
Publisher

Abstract

In this paper, we provide a simple strategy to optimize the performances of a spin chain as a quantum channel for state transfer.We investigate the most general conditions under which a long range interacting chain achieves the highest fidelity and the shortest transfer time. In this respect, we show that the symmetry of the spin chain plys a key role to identify the ideal system, which involves sender and receiver only, and provide numerical evidence. However, the two-spin ideal chain is unpractical due to the decrease of the coupling strength with distance. Therefore we show how to design a spin chain, which nearly approaches the optimal behaviour, while keeping the interaction strength still reasonably high.

DOI
10.1109/icqnm.2009.16

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In this paper, we provide a simple strategy to optimize the performances of a spin chain as a quantum channel for state transfer.We investigate the most general conditions under which a long range interacting chain achieves the highest fidelity and the shortest transfer time. In this respect, we show that the symmetry of the spin chain plys a key role to identify the ideal system, which involves sender and receiver only, and provide numerical evidence. However, the two-spin ideal chain is unpractical due to the decrease of the coupling strength with distance. Therefore we show how to design a spin chain, which nearly approaches the optimal behaviour, while keeping the interaction strength still reasonably high.
We investigate the most general conditions under which a finite ferromagnetic long-range interacting spin chain achieves unitary fidelity and the shortest transfer time in transmitting an unknown input qubit. A deeper insight into system dynamics, allows us to identify an ideal system involving sender and receiver only. However, this two-spin ideal chain is unpractical due to the rapid decrease of the coupling strength with the distance. Therefore, we propose an optimization scheme for approaching the ideal behavior, while keeping the interaction strength still reasonably high. The procedure is scalable with the size of the system and straightforward to implement.
High-quality quantum-state and entanglement transfer can be achieved in an unmodulated spin bus operating in the ballistic regime, which occurs when the endpoint qubits A and B are nonperturbatively coupled to the chain by a suitable exchange interaction j 0 . Indeed, the transition amplitude characterizing the transfer quality exhibits a maximum for a finite optimal value j opt 0 ( N ), where N is the channel length. We show that j opt 0 ( N ) scales as N −1/6 for large N and that it ensures a high-quality entanglement transfer even in the limit of arbitrarily long channels, almost independently of the channel initialization. For instance, for any chain length the average quantum-state transmission fidelity exceeds 90% and decreases very little in a broad neighbourhood of j opt 0 ( N ). We emphasize that, taking the reverse point of view, should j 0 be experimentally constrained, high-quality transfer can still be obtained by adjusting the channel length to its optimal value.
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 calculate the fidelity of transmission of a single qubit between distant sites on semi-infinite and finite chains of spins coupled via the magnetic dipole interaction. We show that such systems often perform better than their Heisenberg nearest-neighbor coupled counterparts, and that fidelities closely approaching unity can be attained between the ends of finite chains without any special engineering of the system, although state transfer becomes slow in long chains. We discuss possible optimization methods, and find that, for any length, the best compromise between the quality and the speed of the communication is obtained in a nearly uniform chain of four spins.
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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.