Fig. 1: Equivalent representations of the protocol.
a Entanglement-based scheme where both Alice and Bob send optimised states with \({n}_{\max }=7\) to Charlie while keeping one arm of their states to themselves denoted as modes A1 and B1, respectively, and measure the number of photons using photon-number resolving detectors (PNRDs). Charlie interferes modes A2 and B2 coming from Alice and Bob and performs a coherent total photon number measurement. b Prepare-and-measure scheme where Alice and Bob send single-mode states to Charlie where they encode the key information on the single mode Fock state one at a time. Charlie then performs a total photon number measurement in his station on the modes that Alice and Bob send.
