High-efficiency and long-distance quantum memory-assisted device-independent quantum secret sharing with single photon sources

TL;DR

The quantum memory-assisted (QMA) DI QSS protocol based on single photon sources (SPSs) is proposed, which achieves the practical key generation efficiency seven orders of magnitude higher than that of the existing DI QSS protocols based on cascaded spontaneous parametric down-conversion sources and six orders of magnitude higher than that of the DI QSS based on SPSs without QMA.

Abstract

Quantum secret sharing (QSS) plays a critical role in building the distributed quantum networks. Device-independent (DI) QSS provides the highest security level for QSS. However, the photon transmission loss and extremely low multipartite entanglement generation rate largely limit DI QSS's secure photon transmission distance (less than 1 km) and practical key generation efficiency. To address the above drawbacks, we propose the quantum memory-assisted (QMA) DI QSS protocol based on single photon sources (SPSs). The single photons from the SPSs are used to construct long-distance multipartite entanglement channels with the help of the heralded architecture. The heralded architecture enables our protocol to have an infinite secure photon transmission distance in theory. The QMA technology can not only increase the multi-photon synchronization efficiency, but also optimize the photon transmittance to maximize the construction efficiency of the multipartite entanglement channels. Our protocol achieves the practical key generation efficiency seven orders of magnitude higher than that of the existing DI QSS protocols based on cascaded spontaneous parametric down-conversion sources and six orders of magnitude higher than that of the DI QSS based on SPSs without QMA. Our protocol has modular characteristics and is feasible under the current experimental technical conditions. Combining with the advanced random key generation basis strategy, the requirement on experimental devices can be effectively reduced. Our protocol is expected to promote the development of long-distance and high-efficiency DI quantum network in the future.

Figures (4)

• Figure 1: (a) Schematic diagram of the QMA SPS DI QSS protocol. The single-photon sources $S_H$ and $S_V$ generate single photons in the horizontal polarization $|H\rangle$ and vertical polarization $|V\rangle$, respectively. The half-wave plate (HWP) realizes $|H\rangle\leftrightarrow|V\rangle$. The quarter-wave plate (QWP) realizes $|H\rangle\rightarrow\frac{1}{\sqrt{2}}(|H\rangle+|V\rangle)$ and $|V\rangle\rightarrow\frac{1}{\sqrt{2}}(|H\rangle-|V\rangle)$. (b) The structure of the three-photon GSM module GSM1. The polarization beam splitter (PBS) can totally transmit $|H\rangle$ polarized photon and reflect $|V\rangle$ polarized photon. The single-photon detectors are used to detect the photons in different output modes. (c) Schematic diagram of the all-optical storage loop QM module QM1. We can control the storage and output of single photon by controlling the "on-off" of the electro-optic modulator (EOM).
• Figure 2: The fully loaded efficiency $E_m$ as a function of photon transmission distance $d$, where the QM storage efficiency is fixed at $\eta_M=100\%$, and the maximum storage pulse interval $N$ is set as $N=0,1,3,5,10$.
• Figure 3: The practical key generation efficiency $E_c$ as a function of the photon transmission distance $d$. Here, we fix the fidelity $F=98\%$, the local efficiency $\eta_l=97.02\%$, the storage efficiency $\eta_M=80\%$, and the maximum storage pulse interval $N=0,1,3,5,10$.
• Figure 4: The practical key generation efficiency $E_c$ of various DI QSS protocols as a function of photon transmission distance $d$. Here, the fidelity is set to $F=98\%$ and the local efficiency to $\eta_l=97.02\%$. For the SPDC DI QSS protocol DIQSS3, the probability of generating a three-photon GHZ state is $10^{-8}$. For QMA SPS DI QSS, the storage efficiency is set to $\eta_M=80\%$.