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arXiv:1301.5610 · Physical Review A

Routing quantum information in spin chains

Simone Paganelli, Salvatore Lorenzo, Tony J. G. Apollaro, Francesco Plastina, Gian Luca Giorgi

Published Jun 10, 2013• 81 citations
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Abstract

Two different models are presented that allow for efficiently performing routing of a quantum state. Both cases involve an $XX$ spin chain working as a data bus and additional spins that play the role of sender and receivers, one of which is selected to be the target of the quantum state transmission protocol via a coherent quantum coupling mechanism making use of local and/or global magnetic fields. Quantum routing is achieved in the first of the models considered by weakly coupling the sender and the receiver to the data bus. On the other hand, in the second model, local magnetic fields acting on additional spins located between the sender and receiver and the data bus allow us to perform high-fidelity routing.

DOI
10.1103/physreva.87.062309

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Two different models are presented that allow for efficiently performing routing of a quantum state. Both cases involve an XXXXXX spin chain working as a data bus and additional spins that play the role of sender and receivers, one of which is selected to be the target of the quantum state transmission protocol via a coherent quantum coupling mechanism making use of local and/or global magnetic fields. Quantum routing is achieved in the first of the models considered by weakly coupling the sender and the receiver to the data bus. On the other hand, in the second model, local magnetic fields acting on additional spins located between the sender and receiver and the data bus allow us to perform high-fidelity routing.
Data multiplexing within a quantum computer can allow for the simultaneous transfer of multiple streams of information over a shared medium thereby minimizing the number of channels needed for requisite data transmission. Here, we investigate a two-way quantum communication protocol using a spin chain placed in an external magnetic field. In our scheme, Alice and Bob each play the role of a sender and a receiver as two states, $\mathrm{cos}(\frac{{\ensuremath{\theta}}_{1}}{2})\left|0\right\ensuremath{\rangle}+\mathrm{sin}(\frac{{\ensuremath{\theta}}_{1}}{2}){e}^{i{\ensuremath{\varphi}}_{1}}\left|1\right\ensuremath{\rangle}$ and $\mathrm{cos}(\frac{{\ensuremath{\theta}}_{2}}{2})\left|0\right\ensuremath{\rangle}+\mathrm{sin}(\frac{{\ensuremath{\theta}}_{2}}{2}){e}^{i{\ensuremath{\varphi}}_{2}}\left|1\right\ensuremath{\rangle}$, are transferred through one channel simultaneously. We find that the transmission fidelity at each end of a spin chain can usually be enhanced by the presence of a second party. This is an important result for establishing the viability of duplex quantum communication through spin chain networks.
Abstract We present an efficient quantum router using a fully-engineered one-dimensional tight-binding array acting as quantum data bus. Quantum routing is achieved by weakly coupling the sender and the receivers to the data bus. We show that perfect transfer of a state between sender and a chosen receiver can be achieved via appropriately tuning the on-site energy applied on the site of the sender. A generalization of this model to the case of multiple receivers is then studied. The results show that the state is equally split between receivers who participate in communication. Moreover, that a similar idea can be used to create WWW state between all receivers is further emphasized.
The transfer of an unknown quantum state, from a sender to a receiver, is one of the main requirements to perform quantum information processing (QIP) tasks. In this respect, the state transfer of a single qubit by means of spin chains has been widely discussed, and many protocols aiming at performing this task have been proposed. Nevertheless, the state transfer of more than one qubit has not been properly addressed so far. In this paper, we present a modified version of a recently proposed quantum state transfer (QST) protocol (Lorenzo S, Apollaro T J G, Sindona A and Plastina F 2013 Phys. Rev. A 87 042313 ) to obtain a quantum channel for the transfer of two qubits. This goal is achieved by exploiting Rabi-like oscillations due to excitations induced by means of strong and localized magnetic fields. We derive exact analytical formulae for the fidelity of the QST and obtain a high-quality transfer for general quantum states as well as for specific classes of states relevant for QIP.
In this paper, we investigate a high-dimensional quantum state transfer protocol. An arbitrary unknown high-dimensional state can be transferred with high fidelity between two remote registers through an XXXXXX coupling spin chain of arbitrary length. The evolution of the state transfer is determined by the natural dynamics of the chain without external modulation and coupling strength engineering. As a consequence, entanglement distribution with a high efficiency can be achieved. Also the strong field and high spin quantum number can partly counteract the effect of finite temperature to ensure the high fidelity of the protocol when the quantum data bus is in the thermal equilibrium state under an external magnetic field.
Routing quantum information among different nodes in a network is a fundamental prerequisite for a quantum internet. While single-qubit routing has been largely addressed, many-qubit routing protocols have not been intensively investigated so far. Building on a recently proposed many-excitation transfer protocol, we apply the perturbative transfer scheme to a two-excitation routing protocol on a network where multiple two-receivers block are coupled to a linear chain. We address both the case of switchable and permanent couplings between the receivers and the chain. We find that the protocol allows for efficient two-excitation routing on a fermionic network, although for a spin-12 network only a limited region of the network is suitable for high-quality routing.
Generating high-quality multiparticle entanglement between communicating parties is the primary resource in quantum teleportation protocols. To this aim, we show that the natural dynamics of a single spin chain is able to sustain the generation of two pairs of Bell states----possibly shared between a sender and a distant receiver---which can in turn enable two-qubit teleportation. In particular, we address a spin-12\frac{1}{2}21​ chain with XXXXXX interactions, connecting two pairs of spins located at its boundaries, playing the roles of sender and receiver. In the regime where both end pairs are weakly coupled to the spin chain, it is possible to generate at predefinite times a state that has vanishing infidelity with the product state of two Bell pairs, thereby providing nearly unit fidelity of teleportation. We also derive an effective Hamiltonian via a second-order perturbation approach that faithfully reproduces the dynamics of the full system.