Scalable and modular generation of multipartite entangled states through memory-enhanced fusion

TL;DR

This work tackles the scalability bottleneck in generating large-scale multipartite entanglement by implementing memory-enhanced fusion between modular quantum memories. By asynchronously preparing two $W_3$ states in spatially separated memory modules and performing on-demand fusion via photonic interference, the authors herald the creation of a four-partite $W$ entangled state across remote memories, which can be converted to a photonic $W$ state for verification. A key result is the linear scaling of fusion efficiency with the tripartite preparation probability $p$, in contrast to the quadratic scaling without memory, enabling more practical scaling to large networks. The demonstrated approach, including entanglement witnesses and potential telecom-band extensions, provides a viable building block toward distributed quantum information processing and scalable quantum networks.

Abstract

Efficient generation of large-scale multipartite entangled states is a critical but challenging task in quantum information processing. Although generation of multipartite entanglement within a small set of individual qubits has been demonstrated, further scale-up in system size requires the connection of smaller entangled states into a larger state in a scalable and modular manner. Here we achieve this goal by implementing memory-enhanced fusion of two multipartite entangled states via photonic interconnects. Through asynchronous preparation of two tripartite W-state entanglements in two spatially-separated modules of atomic quantum memories and on-demand fusion via single-photon interference, we demonstrate the creation of a four-partite W-state entanglement shared by two remote quantum memory modules in a heralded way. We further transfer the W state from the memory qubits to the photonic qubits, and confirm the genuine four-partite entanglement through witness measurements. We then demonstrate memory-enhanced scaling in efficiencies in the entanglement fusion. The demonstrated scalable generation and fusion of multipartite entangled states pave the way towards realization of large-scale distributed quantum information processing in the future.

Figures (8)

• Figure 1: Schematic of the experiment.a, Scale-up of a multipartite entangled state in a modular way under quantum network architecture. Local multipartite entangled states are generated within each individual module. Remote entanglement between modules is established by measurement-induced fusion with the help of quantum interfaces between matter and photonic qubits, which enables the creation of a larger non-local multipartite entanglement. b, Fusion of two tripartite W-state entanglements. Six micro-ensembles are selected as matter qubit carriers from a two-dimensional atomic-ensemble quantum memory array and are divided into two modules. Tripartite W states are sequentially generated within each module. Then one micro-ensemble is chosen from each module, and the stored matter qubits are converted into photonic qubits for single-photon interference (fusion). There are three possible cases in the interference which correspond to three different states of the remaining four matter qubits: (1) successful generation of a four-partite W state; (2) four ensembles in the vacuum state without entanglement; (3) two separate bipartite entangled states. c, The experimental sequence.
• Figure 2: Characterization of two asynchronously prepared tripartite W-state entanglements.a, Schematic of generating and characterizing two $|W_3\rangle$ states in an array of atomic ensembles. b, Population distribution of spin-wave excitations across the three micro-ensembles for the first tripartite W state. The spatial coordinates of the ensembles are (1,1), (1,2), and (1,3). More detailed configuration is illustrated in the Supplementary Information. c, Entanglement witness distribution for the first tripartite W state. A negative value indicates genuine tripartite entanglement. Experimental data confirms that the witness value falls below zero with a probability over $99.99\%$. d,e, Population and entanglement witness for the second tripartite W state.
• Figure 3: Entanglement fusion and the verification of genuine four-partite entanglement.a, Schematic of the entanglement fusion and genuine entanglement verification. b, The measured value for population in zero-, one- and two-excitation subspaces $p_0,\,p_1,\,p_2,$ the fidelity $F$, and the entanglement witness $W_4$ of the four remaining micro-ensembles. Optimal witness in the form of $\mathcal{W}_k=\alpha_k P_0+\beta_k P_1+\gamma_k P_2-|W_N\rangle \langle W_N |$ are given by $\alpha=0.0977$, $\beta=0.7775$, $\gamma=1$. c, Population distribution of spin-wave excitations across the four micro-ensembles for the four-partite W state. d, The distribution of entanglement witness $W_4$. The probability of genuine four-partite entanglement verified by $\text{tr}[\mathcal{W}_4 \rho_e]<0$ is $70.0\%$. e-g, The measured fidelity, population, and entanglement witness for the photonic four-partite W state after post-selection of successful photon detection. Optimal witness parameters are $\alpha^\prime=0.3854$, $\beta^\prime=0.7525$, $\gamma^\prime=0.4101$. The probability of achieving a genuine four-partite entanglement is $95.6\%$ from these measurements.
• Figure 4: Memory-enhanced scaling in generation efficiency of the four-partite W-states. Four-partite entanglement generation efficiency as a function of the success probability $p$ for preparing a tripartite entangled state in each attempt. The blue dots are the measured four-photon coincidence counts per hour, including two signal photons heralding the two successfully prepared tripartite W-states, one heralding photon for the fusion operation, and one readout photon for entanglement verification. The blue solid line denotes the simulated four-photon generation rate in this experiment, while the orange solid line represents the theoretical prediction for a protocol without memory enhancement. The green dotted line shows the simulated enhancement factor between the memory-enhanced and memory-less cases. Error bars represent one standard deviation.
• Figure S1: Experimental configuration and quantum memory performances.a, The experimental setup. b, AOD frequencies for addressing each micro-ensemble and the spatial separations. c, The energy levels used in the experiment. We use the DLCZ protocol to generate atom-photon entanglement. d, Measured end-to-end retrieval efficiency of all the $6$ memory cells with optical transmission losses and detector inefficiencies included. e, Measured cross-correlation function of all the $6$ memory cells.