Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback. (arXiv:1902.02490v2 [quant-ph] UPDATED)

We prove that the classical capacity of an arbitrary quantum channel assisted
by a free classical feedback channel is bounded from above by the maximum
average output entropy of the quantum channel. As a consequence of this bound,
we conclude that a classical feedback channel does not improve the classical
capacity of a quantum erasure channel, and by taking into account energy
constraints, we conclude the same for a pure-loss bosonic channel. The method
for establishing the aforementioned entropy bound involves identifying an
information measure having two key properties: 1) it does not increase under a
one-way local operations and classical communication channel from the receiver
to the sender and 2) a quantum channel from sender to receiver cannot increase
the information measure by more than the maximum output entropy of the channel.
This information measure can be understood as the sum of two terms, with one
corresponding to classical correlation and the other to entanglement.

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