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arXiv:0811.4695 · Physical Review A

Information-transferring ability of the different phases of a finiteXXZspin chain

Abolfazl Bayat, Sougato Bose

Published Jan 6, 2010• 54 citations
arXivHTMLPDF

Abstract

We study the transmission of both classical and quantum information through all the phases of a finite XXZ spin chain. This characterizes the merit of the different phases in terms of their ability to act as a quantum wire. As far as quantum information is concerned, we need only consider the transmission of entanglement as the direct transmission of a quantum state is equivalent. The isotropic AFM spin chain is found to be the optimal point of the phase diagram for the transmission of quantum entanglement when one considers both the amount of transmitted entanglement and the velocity with which it is transmitted. However, this optimal point in the phase diagram moves to the N\'eel phase when decoherence or thermal fluctuations are taken to account. This chain may also be able to transfer classical information even when, due to a large magnitude of the noise, quantum information is not transmitted at all. For a certain range of anisotropies of the model, a curious feature is found in the flow of quantum information inside the chain, namely, a hopping mode of entanglement transfer which skips the odd-numbered sites. Our predictions will potentially be testable in several physical systems.

DOI
10.1103/physreva.81.012304

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We study the transmission of both classical and quantum information through all the phases of a finite XXZ spin chain. This characterizes the merit of the different phases in terms of their ability to act as a quantum wire. As far as quantum information is concerned, we need only consider the transmission of entanglement as the direct transmission of a quantum state is equivalent. The isotropic AFM spin chain is found to be the optimal point of the phase diagram for the transmission of quantum entanglement when one considers both the amount of transmitted entanglement and the velocity with which it is transmitted. However, this optimal point in the phase diagram moves to the N'eel phase when decoherence or thermal fluctuations are taken to account. This chain may also be able to transfer classical information even when, due to a large magnitude of the noise, quantum information is not transmitted at all. For a certain range of anisotropies of the model, a curious feature is found in the flow of quantum information inside the chain, namely, a hopping mode of entanglement transfer which skips the odd-numbered sites. Our predictions will potentially be testable in several physical systems.
We study the information transferring ability of a spin-1∕2 XXZ Hamiltonian for two different proposals of state transfer, namely, the well-studied attaching scenario and the recently proposed measurement induced transport. The latter one has been inspired by recent achievements in optical lattice experiments for local addressability of individual atoms and their time evolution when only local rotations and measurements are available and local control of the Hamiltonian is very limited. We show that while the both scenarios performs with almost similar quality in the case of non-interacting free fermionic XX phase, the difference become more pronounced around the isotropic Heisenberg point. Our study shows that the presence of spin-flip symmetry plays a key point in the quality of state transfer and each scenario which benefits from this symmetry transfers the quantum states with higher fidelity. In fact, for even chains this symmetry exists only for the measurement induced dynamics which then gives higher transport quality and for odd chains the spin-flip symmetry is only valid for the attaching scenarios which become more superior. We also study the effect of thermal fluctuations and environmental interactions on both scenarios.
We study the information transferring ability of a spin-1/2 XXZ Hamiltonian for two different modes of state transfer, namely, the well studied attaching scenario and the recently proposed measurement induced transport. The latter one has been inspired by recent achievements in optical lattice experiments for local addressability of individual atoms and their time evolution when only local rotations and measurements are available and local control of the Hamiltonian is very limited. We show that while measurement induced transport gives higher fidelity for quantum state transfer around the isotropic Heisenberg point, its superiority is less pronounced in non-interacting free fermionic XX phase. Moreover, we study the quality of state transfer in the presence of thermal fluctuations and environmental interactions and show that measurement scheme gives higher fidelity for low temperatures and weak interaction with environment.
Sharing and receiving information plays a pivotal role in science and technology. Quantum communication relies on the principles of quantum mechanics to transmit information in a nonclassical manner. Existing quantum communication protocols are commonly based on shared entangled states between sender and receiver, while the transmitting medium is classical. We here demonstrate that information transfer may be enhanced in a quantum correlated medium without entanglement distribution. We concretely show that nonclassical correlations, with nonzero discord, between the first two spins of a spin chain that acts as a quantum wire can increase the information flow and reduce the propagation time. We relate this effect to the breaking of the spatial symmetry of the out-of-time-order correlator that characterizes the spread of information through the medium.
We address the question of whether there is a way of characterizing the quantum information transport properties of a medium or material. For this analysis, the special features of quantum information have to be taken into account. We find that quantum communication over an isotropic medium, as opposed to classical information transfer, requires the transmitter to direct the signal toward the receiver. Furthermore, for large classes of media there is a threshold, in the sense that 'sufficiently much' of the signal has to be collected. Therefore, the medium's capacity for quantum communication can be characterized in terms of how the sizes of the transmitter and receiver have to scale with the transmission distance to maintain quantum information transmission. To demonstrate the applicability of this concept, an n -dimensional spin lattice is considered, yielding a sufficient scaling of δ n /3 with the distance δ .
We propose a mechanism for perfect entanglement transport in anti-ferromagnetic (AFM) quantum spin chain systems with modulated exchange coupling and also for the modulation of on-site magnetic field. We use the principle of adiabatic quantum pumping process for entanglement transfer in the spin chain systems. We achieve the perfect entanglement transfer over an arbitrarily long distance and a better entanglement transport for longer AFM spin chain system than for the ferromagnetic one. We explain analytically and physically—why the entanglement hops in alternate sites. We find the condition for blocking of entanglement transport even in the perfect pumping situation. Our analytical solution interconnects quantum many body physics and quantum information science.