Distribution of Bell State Entanglement in Qubit Networks via Collision Models

Abstract

We propose a general scheme to controllably distribute pairwise entanglement in a quantum network of qubits by exploiting environmental ancilla qubits interacting with the network nodes through tunable Hamiltonians. Our approach leverages collision models, in which a quantum syatem interacts sequentially with ancilla units. We explore two distinct scenarios within this framework: one in which the ancilla is reset to its initial coherent state after each interaction (the traditional collision model), and another where the ancilla is not reset but its state is simply carried over to the next interaction, which we dub the repeated interaction model. In both scenarios, we ensure that the system-ancilla correlations are discarded between steps. We also demonstrate how varying the ancilla-system interaction patterns enables selective generation of entanglement between different qubit pairs, including non-neighbouring nodes that do not directly interact. The scheme is analyzed in networks up to three qubits under both collision and repeated interaction dynamics, revealing the genaration of maximally entangled bell pairs even in configurations where the interacting ancilla couples to only a single node. Our results provide a systematic and physically implementable route to entanglement distribution, offering potential applications in quantum communication, metrology and modular quantum computing.

Figures (6)

• Figure 1: (Color Online) Illustration of the three-qubit network configurations and the ancilla interaction patterns. The system consists of qubits A, B, and C, with the ancilla qubit designated as 1. (a) Linear chain: Ancilla 1 interacts with a terminal qubit A. (b) Closed-loop (triangular) configuration: Ancilla 1 interacts with qubit A. In both cases, different choices of $H_{\text{S}}$ and $H_{\text{int}}$ influence the entanglement dynamics within the network.
• Figure 2: (Color online) Time evolution of the concurrence $C_\text{BC}(t)$ (- -) for the closed-loop configuration (Fig. \ref{['fig:closed']}), where the ancilla interacts with the qubit A. The network Hamiltonian is $H_\mathrm{S}=\omega_0(\sigma_\text{A}^x \sigma_\text{B}^x+\sigma_\text{B}^x \sigma_\text{C}^x+\sigma_\text{C}^x \sigma_\text{A}^x)$ and the interaction Hamiltonian is $H_\mathrm{int} = \omega\sigma^z_1 \sigma^z_\text{A}$. Parameters: $\omega_0 = 1, \omega = 5, \Delta t = 0.4$. The initial state of the ancilla is $(\ket{0}+\ket{1})/\sqrt{2}.$ The qubit network ABC is initially in the state $\ket{000}.$ The figure illustrates the repeated interaction model (no ancilla reset).
• Figure 3: (Color Online) Time evolution of the concurrence $C_\text{BC}(t)$ (- -) for the linear chain configuration (Fig. \ref{['fig:edge']}), where the ancilla interacts with qubit A. System Hamiltonian is $H_\mathrm{S} = \omega_0(\sigma_\text{A}^x \sigma_\text{B}^x+\sigma_\text{B}^x \sigma_\text{C}^x)$ and interaction Hamiltonian is $H_\mathrm{int} = \omega\sigma^z_1 \sigma^z_\text{A}.$ Parameters: $\omega_0 = 1, \Delta t = 0.4.$ The initial state of the ancilla is $(\ket{0}+\ket{1})/\sqrt{2}.$ The qubit network ABC is initially in the state $\ket{000}.$ In (a) is illustrated the repeated interaction model (no ancilla reset) with $\omega = 5$ and in (b) is illustrated collision model (ancilla reset) with $\omega = 10$.
• Figure 4: (Color Online) Illustration of the three-qubit network, which consists of qubits A, B and C, and the ancilla qubit 1. Ancilla 1 interacts with the middle qubit B in the linear chain.
• Figure 5: (Color online) Time evolution of the concurrence $C_\text{AB}(t)$ ($\bullet$), $C_\text{BC}(t)$ (- -), and $C_\text{AC}(t)$ (---) for the linear chain configuration (Fig. \ref{['fig:middle']}), where the ancilla interacts with the middle qubit B. System Hamiltonian is $H_\mathrm{S} = \omega_0(\sigma_\text{A}^x \sigma_\text{B}^x+\sigma_\text{B}^x \sigma_\text{C}^x)$ and the interaction Hamiltonian is $H_\mathrm{int} = \omega\sigma^z_1 \sigma^z_\text{B}$. Parameters: $\omega_0 = 1, \omega = 5, \Delta t = 0.4$. The initial state of the ancilla is $\ket{1}.$ The qubit network ABC is initially in the state $\ket{000}.$ The figure illustrates both the repeated interaction model (no ancilla reset) and the collision model (ancilla reset).