Matteo Clerici

The ability to generate highly entangled states and access the full quantum state space is crucial for most advanced quantum information tasks. However, in the mid-infrared band, the capability for full state tomography or the demonstration of states that are sufficiently entangled, e.g., to allow positive secure key rates for entanglement-based quantum key distribution (QKD) have not been achieved to date. At a wavelength of 2.1 μm, we demonstrate full state tomography of two-photon states and show near-maximal violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality with an order-of-magnitude improvement over the state of the art in terms of the number of standard deviations above the classical limit. We obtain a positive secure-key rate for the first time using mid-infrared photons (0.417 bits/pair, with a quantum bit error rate of 5.43%) in a proof-of-principle device-independent (DI) QKD scenario, demonstrating the viability of DIQKD at 2.1 μm. We further exploit the quality of the entangled state by obtaining (via computations on the measured state) the violation of a new Bell inequality tailored for a weak or less-rigid form of self-testing, which is of fundamental interest. These results at 2.1 μm pave the way for robust, DI quantum information applications in the mid-infrared region.