General many-body entanglement swapping protocol: opportunities for distributed quantum computing

TL;DR

The paper introduces a general many-body entanglement swapping protocol that enables two non-signaling parties to share high-fidelity, complex multi-qubit states with identical Schmidt vectors to a target state. It analyzes single-intermediary and network configurations, linking fidelity and postselection costs to the target state's Schmidt spectrum via Rényi entropies, and shows how postselection can be avoided or eliminated by spectrum-flattening strategies. The authors provide analytic expressions for Schmidt coefficients and fidelities, and demonstrate a hardware proof-of-concept on IBM quantum devices, including GHZ-state sharing and nonuniform Schmidt-spectrum targets. The approach offers a scalable alternative to pair-based swapping for distributed quantum computing, supports fault-tolerant entanglement swapping through QECCs, and holds promise for robust state sharing across modular quantum processors in the megaquop era.

Abstract

Sharing entangled pairs between non-signaling parties via entanglement swapping constitutes a striking demonstration of the nonlocality of quantum mechanics and a crucial building block for future quantum technologies. In this work, we generalize pair-swapping methods by introducing a many-body entanglement swapping protocol, which allows two non-signaling parties to share general many-body states along an arbitrary partitioning. The shared many-body state retains exactly the same Schmidt vectors as the target state and exhibits typically high fidelity, which approaches unity as the variance of the Schmidt coefficients vanishes. Moreover, we demonstrate how the three-party protocol can be generalized to many-body swapping networks, enabling a general many-body state sharing with unit fidelity via arbitrary number of intermediate nodes. This is achieved by replacing all but one of the unitary operations with those corresponding to the same Schmidt states but with a flattened spectrum, which also completely eliminates the need for postselection. We provide a proof of concept of the three-party protocol on real quantum hardware and discuss how it enables new functionalities, such as fault-tolerant entanglement swapping and new strategies for distributed quantum computing.

Figures (7)

• Figure 1: Many-body entanglement swapping protocol. In step 1, Alice and Bob create locally a target state $|\psi_T\rangle= U|\sigma_0\rangle$ which determines the entanglement structure of the shared state. They share the state along partition in which Alice holds $n_A$ and Bob holds $n_B$ qubits respectively, and send the remaining qubits to Eve. In step 2, Eve applies unitary $U_E$ to her qubits and then measures them. If she obtains result $|\sigma_0\rangle$, she informs Alice and Bob to keep their qubits, otherwise discard them. In step 3, after postselection, Alice and Bob share entangled state $|\psi_{AB}\rangle$ which share exactly the same Schmidt eigenstates as $|\psi_{T}\rangle$ and simply related Schmidt coefficients $\lambda_i^{AB}$.
• Figure 2: Sharing many-body states via many-body swapping in a network with $k$ intermediate nodes. The protocol illustrated here corresponds to the postselection-free implementation discussed in Subsec. \ref{['subsec:postselection']}. In the original version of the protocol (see Subsec. \ref{['subsec:multiple']}), postselection was required based on the measurement outcomes at all intermediate nodes. However, as explained in Subsec. \ref{['subsec:postselection']}, when the Schmidt spectrum is uniform, postselection can be entirely avoided. In this case, each node simply records its measurement outcome and communicates it to Alice, who then applies an appropriate local unitary operation $U_{A,ML}$ on her remaining qubits, resulting in a shared state between Alice and Bob with unit fidelity. Finally, as described in Subsec. \ref{['subsec:general_nonpostselection']}, a similar approach can be applied to states with a non-uniform Schmidt spectrum.
• Figure 3: (a) Circuit for preparing GHZ states. (b) Inverse unitary in the basis where the order of Alice and Bob qubits are switched. (c) Protocol for creating a shared GHZ state for the outermost qubits.
• Figure 4: (a–b) Probability distributions of vector states for the 2- and 3-qubit GHZ states obtained from experimental results on quantum hardware. The error bars represent the standard deviation. (c) GHZ state fidelity as a function of qubit number for three different approaches: (1) ibm_torino, (2) ibm_torino with dynamical decoupling (DD), error mitigation (EM), and (3) Simulation. (d–g) Simulated fidelity decay of GHZ states as a function of qubit number under various noise sources: (d) single-qubit gate errors, (e) ECR gate errors, (f) phase-amplitude damping, and (g) readout errors. See Appendix \ref{['subsec:methods-1']}, for detailed descriptions of the ibm_torino hardware and the noise models used in the simulations.
• Figure 5: Entanglement swapping of states $|\psi_T\rangle=\cos{\frac{\theta}{2}}|00\rangle+ \sin{\frac{\theta}{2}}|11\rangle$ which admits a non-uniform Schmidt spectrum for $0\leq\theta<\pi/2$. (a): Circuit for the swapping protocol. (b) Fidelity of the observed shared state as a function of angle $\theta$. The Ideal line represent the theoretical prediction from Eq. \ref{['eq:overlap2']}