[yyyfb]

I guess not without a minimum bound on the communication speed.

If you have a way to reliably transmit N bits in time T using P photons, you can transmit N+1 bits in time 2 * T using also P photons. What you would do to transmit X0,X1,...Xn is:

- During the first time slot of duration T, transmit X1,... Xn if X0 = 0 and 0 otherwise (assuming absence of photons is one of the symbols, which we can label 0)

- During the second time slot of duration T, transmit 0 if X0=0 and X1,... Xn otherwise

This only uses P photons to transmit one more bit, but it takes twice as long. So if you're allowed to take all the time that you want to transmit, and have really good clocks, I guess that theoretically this is unbounded.