The question is already explained in the title, but I'm curious regarding the possibility to adopt the BB84 protocol over LiFi (in theory). Could it be possible or are there some limitations, such as the single photon evaluation?
Absolutely! BB84 can be implemented over LiFi. There are however certain constraints and inefficiencies involved, which will have to be taken into account for implementation - possibly leading to the usage of BB84 variants like Decoy State, with higher efficiencies than pure BB84.
A four non-orthogonal polarization basis encoded single photon would be very inefficient (mainly loss and complexity of implementation) primarily due to mobility of participants and ambient light noise. We will have to switch to phase encoding, RFI QKD protocol or the decoy state variant of BB84 as an alternate improvement strategy.
Aligning the transmitter and receiver to deliver weak coherent pulses will be challenging, assuming that the transmitter will be handheld or mobile.
The Detector needs to be precisely placed and current cost implications will force us to implement a single detector/multiple transmitter system. This would imply that we have to have a multiplexing (and coordination) strategy for serving individual transmitters. Also, the efficiency shows significant variations on the positioning of the detector in the room (line of sight) and the field of view angle. Losses of the order of 30-50dB have been observed in experimental results.
Hope the insight helps.