Fig. 4.

Encoding and decoding of a short message with twisted light superpositions. The message “Hello World!” is sent letter by letter. Every letter is encoded into three ℓ = ±1 superpositions with four different relative phase settings. For example, the letter “H” is encoded as 0, 2, and 0. Thus, every mode corresponds to 2 bits of information. After 143 km of transmission, the modes are recorded and characterized with an artificial neural network. The same alphabet is used to decode the letter from the mode superpositions. The final recorded message is “Hello WorldP.” The last letter is a “P” (which is encoded as 1,0,0) instead of an “!” (which is encoded as 0,0,0). This error is due to one incorrectly detected mode.