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arXiv:1301.1774 · Physical Review A

Quantum-state transfer via resonant tunneling through local-field-induced barriers

Salvatore Lorenzo, Tony J. G. Apollaro, A. Sindona, Francesco Plastina

Published Apr 9, 2013• 82 citations
arXivHTMLPDF

Abstract

Efficient quantum-state transfer is achieved in a uniformly coupled spin-$1/2$ chain, with open boundaries, by application of local magnetic fields on the second and last-but-one spins, respectively. These effective barriers induce the appearance of two eigenstates, bilocalized at the edges of the chain, which allow a high-quality transfer also at relatively long distances. The same mechanism may be used to send an entire e-bit (e.g., an entangled qubit pair) from one to the other end of the chain.

DOI
10.1103/physreva.87.042313

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Efficient quantum-state transfer is achieved in a uniformly coupled spin-1/21/21/2 chain, with open boundaries, by application of local magnetic fields on the second and last-but-one spins, respectively. These effective barriers induce the appearance of two eigenstates, bilocalized at the edges of the chain, which allow a high-quality transfer also at relatively long distances. The same mechanism may be used to send an entire e-bit (e.g., an entangled qubit pair) from one to the other end of the chain.
We show that an effective two-qubit gate can be obtained from the free evolution of three spins in a chain with nearest neighbor XY coupling, without local manipulations. This gate acts on the two remote spins and leaves the mediating spin unchanged. It can be used to perfectly transfer an arbitrary quantum state from the first spin to the last spin or to simultaneously communicate one classical bit in each direction. One ebit can be generated in half of the time for state transfer. For longer spin chains, we present methods to create or transfer entanglement between the two end spins in half of the time required for quantum state transfer, given tunable coupling strength and local magnetic field. We also examine imperfect state transfer through a homogeneous XY chain.
In a one-dimensional Heisenberg chain, we show that there are no sets of coupling strengths such that the evolution perfectly transfers a quantum state between the two ends of the chain without the addition of magnetic fields. In lieu of perfect transfer, we consider a range of options for achieving high quality transfer, whether in finite time, or via "pretty good" transfer where one waits long times in the hope of getting arbitrarily close to perfect transfer. In attempting to engineer arbitrarily accurate transfer, we explore a new paradigm that facilitates time estimates for achieving any target accuracy εεε for the transfer.
We present an introductory overview of the use of spin chains as quantum wires, which has recently developed into a topic of lively interest. The principal motivation is in connecting quantum registers without resorting to optics. A spin chain is a permanently coupled 1D system of spins. When one places a quantum state on one end of it, the state will be dynamically transmitted to the other end with some efficiency if the spins are coupled by an exchange interaction. No external modulations or measurements on the body of the chain, except perhaps at the very ends, is required for this purpose. For the simplest (uniformly coupled) chain and the simplest encoding (single qubit encoding), however, dispersion reduces the quality of transfer. We present a variety of alternatives proposed by various groups to achieve perfect quantum state transfer through spin chains. We conclude with a brief discussion of the various directions in which the topic is developing.
We present an introductory overview of the use of spin chains as quantum wires, which has recently developed into a topic of lively interest. The principal motivation is in connecting quantum registers without resorting to optics. A spin chain is a permanently coupled 1D system of spins. When one places a quantum state on one end of it, the state will be dynamically transmitted to the other end with some efficiency if the spins are coupled by an exchange interaction. No external modulations or measurements on the body of the chain, except perhaps at the very ends, is required for this purpose. For the simplest ( uniformly coupled) chain and the simplest encoding (single qubit encoding), however, dispersion reduces the quality of transfer. We present a variety of alternatives proposed by various groups to achieve perfect quantum state transfer through spin chains. We conclude with a brief discussion of the various directions in which the topic is developing.