  We propose a new proof method for direct coding theorems for wiretap channels
where the eavesdropper has access to a quantum version of the transmitted
signal on an infinite-dimensional Hilbert space and the legitimate parties
communicate through a classical channel or a classical input, quantum output
(cq) channel. The transmitter input can be subject to an additive cost
constraint, which specializes to the case of an average energy constraint. This
method yields errors that decay exponentially with increasing block lengths.
Moreover, it provides a guarantee of a quantum version of semantic security,
which is an established concept in classical cryptography and physical layer
security. Therefore, it complements existing works which either do not prove
the exponential error decay or use weaker notions of security. The main part of
this proof method is a direct coding result on channel resolvability which
states that there is only a doubly exponentially small probability that a
standard random codebook does not solve the channel resolvability problem for
the cq channel. Semantic security has strong operational implications meaning
essentially that the eavesdropper cannot use its quantum observation to gather
any meaningful information about the transmitted signal. We also discuss the
connections between semantic security and various other established notions of
secrecy.
