  It is well known that ideal free-space optical communication at the quantum
limit can have unbounded photon information efficiency (PIE), measured in bits
per photon. High PIE comes at a price of low dimensional information efficiency
(DIE), measured in bits per spatio-temporal-polarization mode. If only temporal
modes are used, then DIE translates directly to bandwidth efficiency. In this
paper, the DIE vs. PIE tradeoffs for known modulations and receiver structures
are compared to the ultimate quantum limit, and analytic approximations are
found in the limit of high PIE. This analysis shows that known structures fall
short of the maximum attainable DIE by a factor that increases linearly with
PIE for high PIE.
  The capacity of the Dolinar receiver is derived for binary coherent-state
modulations and computed for the case of on-off keying (OOK). The DIE vs. PIE
tradeoff for this case is improved only slightly compared to OOK with photon
counting. An adaptive rule is derived for an additive local oscillator that
maximizes the mutual information between a receiver and a transmitter that
selects from a set of coherent states. For binary phase-shift keying (BPSK),
this is shown to be equivalent to the operation of the Dolinar receiver.
  The Dolinar receiver is extended to make adaptive measurements on a coded
sequence of coherent state symbols. Information from previous measurements is
used to adjust the a priori probabilities of the next symbols. The adaptive
Dolinar receiver does not improve the DIE vs. PIE tradeoff compared to
independent transmission and Dolinar reception of each symbol.

Quantum Physics;Optics