Robust Self-Testing of Multiparticle Entanglement

Quantum self-testing is a device-independent way to certify quantum states and measurements using only the input-output statistics, with minimal assumptions about the quantum devices. Because of the high demand on tolerable noise, however, experimental self-testing was limited to two-photon systems. Here, we demonstrate the first robust self-testing for multiphoton genuinely entangled quantum states. We prepare two examples of four-photon graph states, the Greenberger-Horne-Zeilinger states with a fidelity of 0.957(2) and the linear cluster states with a fidelity of 0.945(2). Based on the observed input-output statistics, we certify the genuine four-photon entanglement and further estimate their qualities with respect to realistic noise in a device-independent manner.

Figure 1

Four-party Bell inequalities: In each round of Bell inequalities, each party receives a classical bit $w$, $x$, $y$, $z$ and output a classical bit $a$, $b$, $c$, $d$. A score is obtained according to the conditional probabilities $P(abcd|wxyz)$ and a predetermined rule.

Figure 2

The experimental setup. A pulsed Ti-sapphire laser as the pump beam (repetition rate 80 MHz, center wavelength 775 nm, an average power $\sim 0.9\mathrm{W}$, temporal duration $\sim 130\mathrm{fs}$) passes through an optical isolator and half-wave plate (HWP, 775 nm) and then is split into two beams by a dual-wavelength polarizing beam splitter (dPBS, $775/1550\mathrm{nm}$). Two periodically poled KTiOPO4 (ppKTP) crystals in polarization-based Sagnac Interferometers are pumped by the split pump beams for producing polarization-entangled photon pairs [43, 44]. The remaining pump lights are removed by dichroic mirrors (DM). Fine adjustments of the delays between different paths are made so that the photons arrive at the polarizing beam splitter or polarization dependent beam splitter simultaneously. When there is only one photon in each path after PBS1 (or PDBS) and conditionally on the fourfold coincidences [46, 47], we obtain a four-photon GHZ state (or linear cluster state). All the photons are spectrally filtered by filters and the outputs are detected by superconducting nanowire single photon detectors with average detector efficiency of 79% where all the four-photon coincidences are recorded by a multichannel coincidence count unit. QWP and dHWP represent quarter wave plate and dual-wavelength half-wave plate.

Figure 3

Minimum fidelity $F$ to the target graph state versus various Bell inequality values $⟨{\mathcal{B}}_1⟩\sim ⟨{\mathcal{B}}_6⟩$. The dashed line $(F=1/2)$ is the boundary between the genuine entanglement $(F>1/2)$ and inconclusive $(F\le 1/2)$. The green, blue, and red dots indicate different noisy proportion $p=0$, $p=0.1$, and $p=0.2$, respectively. Error bars indicate one standard deviation deduced from propagated Poissonian counting statistics of the raw detection events.