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arXiv:2604.01773 · Physics Letters A

Distribution of Bell State Entanglement in Qubit Networks via Collision Models

Elif Yunt, Mert Doğan, Öner Faruk Ödemiş, Özgür E. Müstecaplıoğlu

quant-phSubmitted Apr 2, 2026• Announced Apr 3, 2026• 0 citations• Revised Sep 7, 2026 (v2)
v1 · Apr 2, 2026v2 · Sep 7, 2026
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Abstract

We investigate the selective generation of Bell-pair entanglement in three qubit networks using a standard quantum collision model. By varying the network geometry, the node contacted by the ancilla, and the interaction Hamiltonians, we identify configurations in which high pairwise concurrence and Bell state fidelity are generated between different target qubits, including nonadjacent qubits and qubits not directly coupled to the ancilla. For comparison, we also consider the continuous time unitary evolution of the complete ancilla network system, sampled at the same discrete time intervals. This reference calculation clarifies how discarding each outgoing ancilla and removing its correlations from subsequent dynamics modifies the attainable entanglement and preparation time. Our results provide a proof of principle demonstration of geometry dependent Bell pair generation and routing in small qubit networks.

DOI
10.1016/j.physleta.2026.132139
Comments
9 pages, 7 figures, final version

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We investigate the selective generation of Bell-pair entanglement in three qubit networks using a standard quantum collision model. By varying the network geometry, the node contacted by the ancilla, and the interaction Hamiltonians, we identify configurations in which high pairwise concurrence and Bell state fidelity are generated between different target qubits, including nonadjacent qubits and qubits not directly coupled to the ancilla. For comparison, we also consider the continuous time unitary evolution of the complete ancilla network system, sampled at the same discrete time intervals. This reference calculation clarifies how discarding each outgoing ancilla and removing its correlations from subsequent dynamics modifies the attainable entanglement and preparation time. Our results provide a proof of principle demonstration of geometry dependent Bell pair generation and routing in small qubit networks.
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By means of composite quantum collision models, we study the entanglement dynamics of a bipartite system, i.e., two qubits S 1 and S 2 interacting directly with an intermediate auxiliary qubit S A, while S A is in turn coupled to a thermal reservoir. We are concerned with how the intracollisions of the reservoir qubits influence the entanglement dynamics. We show that even if the system is initially in the separated state, their entanglement can be generated due to the interaction between the qubits. In the long-time limit, the steady-state entanglement can be generated depending on the initial state of S 1 and S 2 and the environment temperature. We also study the dynamics of tripartite entanglement of the three qubits S 1, S 2, and S A when they are initially prepared in the GHZ state and separated state, respectively. For the GHZ initial state, the tripartite entanglement can be maintained for a long time when the collision strength between the environment qubits is sufficiently large.
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We study the entanglement dynamics of a family of quantum collision models by analytically solving the pairwise concurrence for all qubit pairs. We introduce a diagrammatic method that offers an intuitive, frame-by-frame understanding of these dynamics. This allows us to monitor how a single collision affects the entanglement of the whole many-body system in some special cases. We focus on a class of models where the square of concurrence is a conserved quantity in the qubit collisions, aiding us to formulate general rules of entanglement propagation. In particular, among the multiple examples we will be showing, we identify a type of genuine multipartite entanglement, which we refer to as \textit{entanglement quilt}, where every qubit is entangled with every other qubit. We find that in some models, an entanglement quilt is hypersensitive to local excitation fluctuations: The presence of even a single excited qubit can destroy the entanglement quilts. We offer a detailed mathematical treatment on the phenomena, which can help us understand the disappearance of long-range entanglement in condensed matter systems above zero temperature. We also speculate about a possible property of the entanglement quilt: Every subsystem of it is entangled with every other subsystem.
We investigate entanglement distribution in pure-state quantum networks. We consider the case when nonmaximally entangled two-qubit pure states are shared by neighboring nodes of the network. For a given pair of nodes, we investigate how to generate the maximal entanglement between them by performing local measurements, assisted by classical communication, on the other nodes. We find optimal measurement protocols for both small and large one-dimensional networks. Quite surprisingly, we prove that Bell measurements are not always the optimal ones to perform in such networks. We generalize then the results to simple small two-dimensional (2D) networks, finding again counterintuitive optimal measurement strategies. Finally, we consider large networks with hierarchical lattice geometries and 2D networks. We prove that perfect entanglement can be established on large distances with probability one in a finite number of steps, provided the initial entanglement shared by neighboring nodes is large enough. We discuss also various protocols of entanglement distribution in 2D networks employing classical and quantum percolation strategies.
Quantum networks are designed to transmit quantum bits (qubits) among quantum devices to enable new network resources for the applications. Entanglement distribution and entanglement swapping are fundamental procedures that are required in several network operations. However, they are probabilistic operations, which can lead to severe network performance degradation. This article investigates the engineering problem of resource allocation in quantum networks, considering factors like entanglement distribution probability, quantum memory characteristics, and fidelity. We model this as an optimization model to obtain an optimal solution. In particular, we formulate an integer linear programming (ILP) and develop a heuristic algorithm, aiming to minimize the number of required entangled qubit pairs (Bell pairs or EPR pairs) in any adjacent pair in the quantum network. Extensive simulations are performed to compare the performance of proposed ILP and heuristic. In all the cases, the heuristic produces a comparable solution to the optimal one. Simulation results ensure that the value of maximum utilized Bell pairs in a quantum network highly depends on the value of the probability of entangled pairs established, considering the time in the quantum memory besides the number of incoming requests.