The capacity of the photon counting channel

Previous work has shown that the capacity of the single-mode photon-counting channel in the region in which quantum effects are most pronounced is
1/(kT \ln 2)
bit/J. Here
T
is the quantum noise temperature, and
k
is Boltzmann's constant. However, to achieve this, the number of photons per second must be very low, so this does not determine the capacity of the average power-limited photon channel in bits per second. Here the previous work is extended and the capacity is determined in bits per second. This includes a determination of the optimum counting time. The capacity in bits per second is for low
T
asymptotic to
P_{s}/(kT \ln 2)
, where
P_{s}
is the average signal power. This is high enough to suggest that photon counting be seriously considered for applications such as a deep space to near Earth link. Some related problems are also considered including a peak power limitation.