Experimental Multipartite Entanglement Detection With Minimal-Size Correlations

Abstract

Multiparticle entanglement is a valuable resource for quantum technologies, including measurement based quantum computing, quantum secret sharing, and a variety of quantum sensing applications. The direct way to detect this resource is to observe correlations arising from local measurements performed simultaneously on all particles. However, this approach is increasingly vulnerable to measurement imperfections when the number of particles grows, and becomes unfeasible for large-scale entangled states. It is therefore crucial to devise detection methods that minimize the number of simultaneously measured particles. Here we provide the first experimental demonstration of multipartite entanglement detection with minimal-size correlations, showing that our setup is robust to misalignment of the local measurement bases and enables the certification of genuine multipartite entanglement in a regime where the direct approach fails. Overall, our results indicate a promising route to the experimental detection of genuine multipartite entanglement in large-scale entangled states.

Figures (7)

• Figure 1: Entanglement detection length (EDL) is the minimum number of parties that must be jointly measured to certify a state’s genuine multipartite entanglement (GME). For example, the EDL for a W state is $2$, whereas the EDL for a cluster state is $3$. (a) For the $3$-qubit W state, we consider two EDL witnesses, ${\cal W}_1$ and ${\cal W}_2$, constructed from two‑body joint measurements over the pairs $\{12, 23\}$ and $\{12, 23, 13\}$, respectively. (b) For the $4$-qubit cluster state, we consider two EDL witnesses, ${\cal W}_1$ and ${\cal W}_3$, constructed from three‑body joint measurements over the triplets $\{124, 134\}$ and $\{124, 234, 134\}$, respectively.
• Figure 2: Experimental setup. A mode-locked Ti:sapphire laser (775 nm, 80 MHz) pumps a periodically poled KTiOPO$_4$ (ppKTP) crystal, producing photon pairs via type-II spontaneous parametric down-conversion (SPDC). An optical isolator directly after the laser suppresses back-reflections. Residual pump light is removed with a dichroic mirror (DM), and temporal walk-off is compensated using a potassium dihydrogen phosphate (KDP) crystal. After spectral filtering with interference filters (IFs), two-photon interference is implemented on beam-splitter / polarization-dependent beam-splitter (BS/PDBS) networks; the interphoton delay is tuned by a motorized translation stage to ensure temporal overlap. Each output mode is analyzed by a standard quarter-wave-plate–half-wave-plate–polarizing-beam-splitter (QWP–HWP–PBS) module implementing the required local projective settings. Photons are coupled into single-mode fibers (SMFs) and detected with superconducting nanowire single-photon detectors (SNSPDs, $\approx 90\%$ efficiency); fourfold coincidences are recorded with a multichannel coincidence counter. Here, dHWP and dPBS denote a dual-wavelength half-wave plate (775/1550 nm) and a dual-wavelength polarizing beam splitter (775/1550 nm), respectively. (a) Four-photon Dicke and heralded three-photon $W$ states. (b) Four-photon $W$ states. (c) Four-photon cluster states.
• Figure 3:
• Figure 4: Experimental results. (a) Four-photon Dicke states; (b) three-photon W states; (c) four-photon W states; (d) four-photon cluster states. Bars show measured witness values, with bar colors denoting the experimentally prepared entangled-state fidelities; an ideal $F=1$ reference is included for comparison. The red dashed zero line marks the GME threshold (negative values certify genuine multipartite entanglement). EDL-constructed witnesses ${\cal W}_i$ are shown together with their predicted maximum tolerable white-noise fractions $p_i$. Error bars indicate one standard deviation obtained by propagating Poissonian counting statistics of the raw counts.
• Figure 5: Two-photon quantum state tomography of the entanglement source, which generate a state $|\psi>=\frac{1}{\sqrt2}(|HH\rangle+|VV\rangle)$. Realpart on the left, and imaginary part on the right.