It needs to be pointed out that the diode isn't converting over 100% of the electrical power into optical power. The extra optical power comes from Peltier heat drawn from the semiconductor lattice. The LEDs only had ">100% efficiency" when heated to 135°C. At 25°C the electrical efficiency was less than 1%.[1]
[1] Fig 1 (a) https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.108.097...