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arXiv:1812.11609 · Physical Review A

Spin chains for two-qubit teleportation

Tony J. G. Apollaro, G. M. A. Almeida, Salvatore Lorenzo, Alessandro Ferraro, Simone Paganelli

Published Nov 6, 2019• 30 citations
arXivHTMLPDF

Abstract

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-$\frac{1}{2}$ chain with $XX$ 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.

DOI
10.1103/physreva.100.052308

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We revisit the teleportation of two qubits entanglement using a single channel made of a single Majorana wire connecting two pairs of qubits each at the sending and receiving ends of the wire. The scheme is different from that use in our early work (Phys. Scr. 95 035803 (2020)) where the two qubit teleportation required two copies of the Majorana wires setup as required to implement the Lee and Kim teleportation scheme. The two pairs of qubit interact via the exchange coupling. It is in this setting that we investigate the role of the exchange coupling, the channel parameters, the spin chain parameters on the average fidelity of entanglement teleportation. We equally consider the fact that the geographically located two pairs of qubits interact differently with their respective spin chain environment. The dynamics of the average fidelity is shown to be enhanced when using a set-up with symmetric coupling between qubits and Majorana wire at both ends as compared to when using asymmetric coupling. Small values of the coupling between the qubits and spin environments should however be used. Large values of the exchange coupling between qubits in the two sub-systems should be used to have high fidelity of the teleported state. The dynamics of the average fidelity of entanglement teleportation is seen to depend on the size of the spin environment as compared to the teleportation protocol used in our earlier work where the dynamics is mildly sensitive to the size of the spin environment. Increasing the strength of the transverse magnetic field and large values of the anisotropy degree enhances the average fidelity of entanglement teleportation. The same observation is seen when considering the same values of the coupling between the two qubits sub-systems at the opposite ends of the Majorana wire and their respective spin environment. The dynamics of the system is however seen to observe almost a similar trend as that of the above cited work for the single Majorana wire setup.
We propose a protocol for state transfer and entanglement generation between two distant spin qubits (sender and receiver) that have different energies. The two qubits are permanently coupled to a far-off-resonant spin chain, and the qubit of the sender is driven by an external field, which provides the energy required to bridge the energy gap between the sender and the receiver. State transfer and entanglement generation are achieved via virtual single-photon and multiphoton transitions to the eigenmodes of the channel.
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.
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We explore the capability of spin-1/2 chains to act as quantum channels for both teleportation and transfer of qubits. Exploiting the emergence of long-distance entanglement in low-dimensional systems [Phys. Rev. Lett. 96, 247206 (2006)10.1103/Phys.Rev.Lett.96, 247206(2006)], here we show how to obtain high communication fidelities between distant parties. An investigation of protocols of teleportation and state transfer is presented, in the realistic situation where temperature is included. Basing our setup on antiferromagnetic rotationally invariant systems, both protocols are represented by pure depolarizing channels. We propose a scheme where channel fidelity close to 1 can be achieved on very long chains at moderately small temperature.