A scheme for quantum teleportation between discrete and continuous encodings of an optical qubit

Transfer of quantum information between physical systems of a different nature is a central matter in quantum technologies. Particularly challenging is the transfer between discrete- and continuous degrees of freedom of various harmonic oscillator systems. Here we implement a protocol for teleporting a continuous-variable optical qubit, encoded by means of coherent states, onto a discrete-variable, single-rail qubit - a superposition of the vacuum- and single-photon optical states - via a hybrid entangled resource. We test our protocol on coherent states of different phases and obtain the teleported qubit with a fidelity of $0.83\pm0.04$. We also find that the phase of the resulting qubit varies consistently with that of the input, having a standard deviation of $3.8^\circ$ from the target value. Our work opens up the way to wide application of quantum information processing techniques where discrete- and continuous-variable encodings are combined within the same optical circuit.