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arXiv:2011.13711 · Entropy

Two-Excitation Routing via Linear Quantum Channels

Tony J. G. Apollaro, Wayne Jordan Chetcuti

Published Dec 31, 2020• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.3390/e23010051

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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.
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.
For several decades, scientists have been aware of significant benefits allowing quantum information processing technologies to surpass their classical counterparts. Recent technological development allows these benefits to be tested experimentally and in some cases also implemented in practical devices. So far the majority of experimental quantum networks was limited to peer-to-peer communications between two parties. Practical implementation of quantum communications networks, however, needs to address the problem of scalability to serve large numbers of users. Similarly to classical computer networks, their quantum counterparts would require routing protocols to direct the signal from its source to destination. Devices implementing these routing protocols are called quantum routers and have recently been subject of an intense research. In this paper, we report on experimental implementation of a linear-optical quantum router. Our device allows single-photon polarization-encoded qubits to be routed coherently into two spatial output modes depending on the state of two identical control qubits. The polarization qubit state of the routed photon is maintained during the routing operation. The success probability of our scheme can be increased up to 25% making it the most efficient linear-optical quantum router developed to this date.
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.
We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-12\frac{1}{2}21​ network, on a lattice of any dimensionality. Under the assumptions that the network Hamiltonian preserves the magnetization and that a fully polarized initial state is taken for the lattice, we obtain a general formula for the average fidelity of the two qubits QST, linking it to the one- and two-particle transfer amplitudes of the spin excitations among the sites of the lattice. We then apply this formalism to a 1D spin chain with XXXXXX-Heisenberg type nearest-neighbour interactions adopting a protocol that is a generalization of the single qubit one proposed in Paganelli et al. [Phys. Rev. A 87, 062309 (2013)]. We find that a high-quality two qubit QST can be achieved provided one can control the local fields at sites near the sender and receiver. Under such conditions, we obtain an almost perfect transfer in a time that scales either linearly or, depending on the spin number, quadratically with the length of the chain.
Motivated by the need for quantum computers to communicate between multiple, well separated qubits, we introduce the task of quantum routing for distributing quantum states, and generating entanglement, between these sites. We describe regular families of coupled quantum networks which perfectly route qubits between arbitrary pairs of nodes with a high transmission rate. The ability to route multiple states simultaneously and the regularity of the networks vastly improve the utility of this scheme in comparison to the task of state transfer, leading us to propose an implementation in optical lattices.
In recent years, quantum communication networks have emerged as a promising alternative to classical communication networks for the transmission of quantum information. One of the challenges for achieving optimal performance in quantum communication networks is the efficient routing of quantum signals across multiple paths. To address this, a variety of routing protocols have been proposed, including multi-path routing protocols. Multi-path routing involves sending a quantum signal through multiple distinct paths simultaneously to reduce delays in the transmission of quantum information. By distributing the quantum information over multiple paths, this approach can provide significant performance improvements, including reduced latency and higher throughput. In addition, multi-path routing can enable new possibilities for the security of quantum communication networks, such as more secure entanglement swapping protocols and improved protection against eavesdropping. In this paper, we investigate the performance of multi-path routing protocols in multi-node quantum communication networks. We consider two approaches to multi-path routing, a basic routing approach based on shortest path optimization, and a more advanced approach based on graph partitions. We evaluate the performance of these protocols in a range of multi-node networks, with focus on the trade-off between latency and throughput. The results show that multi-path routing yields significant performance improvements in such networks and provides an efficient way for routing quantum signals across multiple paths.