Modelling Quantum Transduction for Multipartite Entanglement Distribution

TL;DR

This work targets multipartite entanglement distribution for a Quantum Internet by bridging superconducting qubits and optical channels through quantum transduction. It compares Direct Multipartite Distribution (DMD) with Teleported Multipartite Distribution (TMD) and develops a transducer-performance framework to analyze four TMD variants: vanilla, intrinsic-entanglement (IE-TMD), and entanglement-swapping (IES-TMD, plus a swapping extension). Key results show that DMD faces fundamental capacity constraints due to entanglement persistence and transduction losses, while vanilla-TMD provides nonzero capacity for any nonzero link success probability $p^v_c$; IE-TMD relaxes cooperativity requirements by generating entanglement intrinsically, though not achieving unit capacity, and IES-TMD enables heralded entanglement via detector clicks at the cost of added hardware and still subunit maximum capacity. The study emphasizes that conversion efficiency and cooperativity critically shape performance, suggesting a standardized QT model based on conversion-efficiency to compare hardware across platforms and to guide future quantum-network design.

Abstract

Superconducting and photonic technologies are envisioned to play a key role in the Quantum Internet. However the hybridization of these technologies requires functional quantum transducers for converting superconducting qubits, exploited in quantum computation, into ``flying'' qubits, able to propagate through the network (and vice-versa). In this paper, quantum transduction is theoretically investigated for a key functionality of the Quantum Internet, namely, multipartite entanglement distribution. Different communication models for quantum transduction are provided, in order to make the entanglement distribution possible. The proposed models departs from the large heterogeneity of hardware solutions available in literature, abstracting from the particulars of the specific solutions with a communication engineering perspective. Then, a performance analysis of the proposed models is conducted through key communication metrics, such as quantum capacity and entanglement generation probability. The analysis reveals that -- although the considered communication metrics depend on transduction hardware parameters for all the proposed models -- the particulars of the considered transduction paradigm play a relevant role in the overall entanglement distribution performance.

Figures (13)

• Figure 1: Direct Multipartite entanglement Distribution (DMD) for a $3$-qubit GHZ state. The multipartite state is generated locally at the superconducting orchestrator, and it must be distributed to the superconducting nodes representing the three clients via optical quantum channels. Ebits at microwave and optical frequencies are depicted in blue and red, respectively. The Quantum Transducers (QTs) at the orchestrator realize an up-conversion of the ebits of the GHZ state, by converting them from microwave to optical frequencies. After being distributed through optical channels, the ebits are converted again into microwave frequencies with a down-conversion process implemented by the QTs at the clients.
• Figure 2: Network state before EPR pairs distribution: the orchestrator locally generates the multipartite state as well as additional microwave EPR pairs -- one for each ebit of the multipartite state that must be distributed to the clients -- that are distributed through up- and down-conversion processes, while no conversion are required for the multipartite state.
• Figure 3: Network state after EPR pairs distribution: EPR pairs have been distributed (ideally) so that one microwave ebit is at the orchestrator and the other microwave ebit is at each client. By consuming the EPR pairs during the teleportation processes, each microwave ebit of the multipartite state -- a $3$-qubit GHZ state in this case -- is teleported at the corresponding client
• Figure 5: Conversion efficiency $\eta$ as a function of cooperativity $C$ and the product of extraction ratios $\zeta_o\zeta_m$.
• Figure 6: DMD & vanilla-TMD: ebit distribution probability $p^v_c$ between the orchestrator and the arbitrary client $c$ as a function of cooperativity $C$ and link length $l_{o,c}$. The probability has been computed by reasonably assuming similar transduction hardware for both up- and down-conversion -- i.e., $C=C_{\uparrow}=C_{\downarrow}$ -- and by considering ideal extraction ratios -- i.e., $\zeta_o = \zeta_m = 1$. The dotted black line denotes the contour plot for $p^v_c = \frac{1}{2}$.

Theorems & Definitions (11)

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