Experimental quantum triangle network nonlocality with an AlGaAs multiplexed entangled photon source

TL;DR

This work tackles network nonlocality in triangle configurations without inputs by deriving a noise-robust Bell-like inequality that remains applicable under arbitrarily strong correlations between sources. It proposes an $\epsilon_1$-trilocal framework and a practical quantum strategy using an AlGaAs broadband entangled-photon source, with a robust generalization incorporating $\Delta$ to account for imperfect correlations. The authors experimentally implement a simulated triangle network by spectrally multiplexing one broadband source into three channel pairs and engineering a partially entangled AB state, achieving high state fidelities and strong source correlations, and they demonstrate violation of the Bell-like inequality across a broad parameter region, quantified by a p-value well below 0.05 and mutual information analyses showing near-zero cross-channel correlations. The results deepen understanding of network nonlocality under realistic conditions and highlight a scalable, fiber-compatible platform for quantum networks with potential device-independent certification in the future.

Abstract

The exploration of the concept of nonlocality beyond standard Bell scenarios in quantum network architectures unveils fundamentally new forms of correlations that hold a strong potential for future applications of quantum communication networks. To materialize this potential, it is necessary to adapt theoretical advances to realistic configurations. Here we consider a quantum triangle network, for which is was shown in theory that, remarkably, quantum nonlocality without inputs can be demonstrated for sources with an arbitrarily small level of independence. We realize experimentally such correlated sources by carefully engineering the output state of a single AlGaAs multiplexed entangled-photon source, exploiting energy-matched channels cut in its broad spectrum. This simulated triangle network is then used to violate experimentally for the first time a Bell-like inequality that we derive to capture the effect of noise in the correlations present in our system. We also rigorously validate our findings by analysing the mutual information between the generated states. Our results allow us to deepen our understanding of network nonlocality while also pushing its practical relevance for quantum communication networks.

Figures (8)

• Figure 1: Scheme of a simulated triangle network using one physical source whose spectrum is multiplexed into three energy-matched frequency channels. The three states $\rho_{BC}$, $\rho_{AC}$, and $\rho_{AB}$ shared between Bob and Charlie, Alice and Charlie and Alice and Bob, respectively, are associated with a local hidden variable $\alpha$, $\beta$, and $\gamma$ respectively. The possible correlations between them are taken into account by introducing a fourth local hidden variable $\lambda$.
• Figure 2: Sketch of the experimental setup for the implementation of the triangle network using a single source of broadband multiplexed entangled photon states, showing the generation, demultiplexing, quantum state engineering, and polarization analysis stages. The transmission window (in nm) for each filter is as follows: red channel $[1544.8,1550.75] \cup [1538.5,1544.45]$, blue channel $[1550.9, 1553.9] \cup [1535.4, 1538.34]$, and green channel $[1554, 1557.1] \cup [1532.3, 1535.2]$. P: Polarizer; MO: Microscope objective; LPF: Long-Pass Filter; WSS: Waveshaper Selective Switch; FPC: Fiber Polarization Controller; PDL: Polarization Dependent Loss; PBS: Polarizing Beam Splitter; SNSPD: Superconducting Nanowire Single Photon Detector; TDC: Time-to-Digital Converter
• Figure 3: Theoretical (a) and experimental (b) quantum distribution $p(a_B,b_A,a_C,b_C)$. The first is derived by considering perfect sources $\rho_{AB}$, $\rho_{AC}$, and $\rho_{BC}$ as defined in Eqs.\ref{['Perfect_State1']} and \ref{['Eberhard_state']}. $(a_B,a_C)$ and $(b_A,b_C)$ represent the outcomes obtained by Alice and Bob, respectively. Each color corresponds to a basis projection for the state $\rho_{AB}$, defined by the output $(a_C,b_C)$.
• Figure 4: (a) $S_\Delta$ parameter deduced from the experimental results as a function of $\epsilon_1$ and $\epsilon_2$. The yellow surface above the grey plane $S_\Delta=0$ defines the region $\epsilon_1\times\epsilon_2$ where the Bell-like inequality is violated. (b) Corresponding statistical significance estimated via the p-value. A p-value lower than the threshold value of $0.05$ confirms the rejection of a LHV model.
• Figure 5: Polarization basis used by Alice and Bob for measuring the state $\rho_{AB}$. The angle $\varphi$ corresponds to $\varphi_{A(B)}$ for Alice (Bob).