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arXiv:quant-ph/0312141 · Physical Review A

Propagation of quantum information through a spin system

Tobias J. Osborne, Noah Linden

Published May 14, 2004• 236 citations
arXivHTMLPDF

Abstract

It has been recently suggested that the dynamics of a quantum spin system may provide a natural mechanism for transporting quantum information. We show that one-dimensional rings of qubits with fixed (time-independent) interactions, constant around the ring, allow high-fidelity communication of quantum states. We show that the problem of maximizing the fidelity of the quantum communication is related to a classical problem in Fourier wave analysis. By making use of this observation we find that if both communicating parties have access to limited numbers of qubits in the ring (a fraction that vanishes in the limit of large rings) it is possible to make the communication arbitrarily good.

DOI
10.1103/physreva.69.052315

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It has been recently suggested that the dynamics of a quantum spin system may provide a natural mechanism for transporting quantum information. We show that one-dimensional rings of qubits with fixed (time-independent) interactions, constant around the ring, allow high-fidelity communication of quantum states. We show that the problem of maximizing the fidelity of the quantum communication is related to a classical problem in Fourier wave analysis. By making use of this observation we find that if both communicating parties have access to limited numbers of qubits in the ring (a fraction that vanishes in the limit of large rings) it is possible to make the communication arbitrarily good.
We investigate quantum communication between the sites of a spin ring with twisted boundary conditions. Such boundary conditions can be achieved by a magnetic flux through the ring. We find that a nonzero twist can improve communication through finite odd-numbered rings and enable high-fidelity multiparty quantum communication through spin rings (working near perfectly for rings of five and seven spins). We show that in certain cases, the twist results in the complete blockage of quantum-information flow to a certain site of the ring. This effect can be exploited to interface and entangle a flux qubit and a spin qubit without embedding the latter in a magnetic field.
We shall consider a quantum communication channel constituted by two open spin chains with nearest neighbour interactions and fixed coupling strengths, connected to several users. Assuming that the users of this quantum data bus can apply simple gates on sites of the chain that they are connected to, we will see that it is possible to gain information on the position of the qubit during the transmission, and to use this information to accelerate the communication process. We will also see that performing frequent measurements on the system affects the dynamics of propagation of quantum information in an interesting way.
The last decade has witnessed substantial interest in protocols for transferring information on networks of quantum mechanical objects. A variety of control methods and network topologies have been proposed, on the basis that transfer with perfect fidelity-i.e., deterministic and without information loss-is impossible through unmodulated spin chains with more than a few particles. Solving the original problem formulated by Bose [Phys. Rev. Lett. 91, 207901 (2003)], we determine the exact number of qubits in unmodulated chains (with an XY Hamiltonian) that permit transfer with a fidelity arbitrarily close to 1, a phenomenon called pretty good state transfer. We prove that this happens if and only if the number of nodes is n = p - 1, 2p - 1, where p is a prime, or n = 2(m) - 1. The result highlights the potential of quantum spin system dynamics for reinterpreting questions about the arithmetic structure of integers and, in this case, primality.
Propagation of information encoded in spin degrees of freedom through networks of coupled spins enables important applications in spintronics and quantum information processing. We study control of information propagation in networks of spin-1/2 particles with uniform nearest neighbor couplings forming a ring with a single excitation in the network as simple prototype of a router for spin-based information. Specifically optimizing spatially distributed potentials, which remain constant during information transfer, simplifies the implementation of the routing scheme. However, the limited degrees of freedom makes finding a control that maximizes the transfer probability in a short time difficult. We show that the structure of the eigenvalues and eigenvectors must fulfill a specific condition to be able to maximize the transfer fidelity, and demonstrate that a specific choice among the many potential structures that fulfill this condition significantly improves the solutions found by optimal control.
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.
One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet there are ways of conveying information with exponentially fewer qubits than possible classically. Moreover, these methods have a very simple structure---they involve little interaction between the communicating parties. We look more closely at the ways in which information encoded in quantum states may be manipulated, and consider the question as to whether every classical protocol may be transformed to a ``simpler'' quantum protocol of similar efficiency. By a simpler protocol, we mean a protocol that uses fewer message exchanges. We show that for any constant k, there is a problem such that its k+1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity, thus answering the above question in the negative. Our result builds on two primitives, local transitions in bi-partite states (based on previous work) and average encoding which may be of significance in other applications as well.