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Secure communication over fully quantum Gel'fand-Pinsker wiretap channel
In this work we study the problem of secure communication over a fully
quantum Gel'fand-Pinsker channel. The best known achievability rate for this
channel model in the classical case was proven by Goldfeld, Cuff and Permuter
in [Goldfeld, Cuff, Permuter, 2016]. We generalize the result of [Goldfeld,
Cuff, Permuter, 2016]. One key feature of the results obtained in this work is
that all the bounds obtained are in terms of error exponent. We obtain our
achievability result via the technique of simultaneous pinching. This in turn
allows us to show the existence of a simultaneous decoder. Further, to obtain
our encoding technique and to prove the security feature of our coding scheme
we prove a bivariate classical-quantum channel resolvability lemma and a
conditional classical-quantum channel resolvability lemma. As a by product of
the achievability result obtained in this work, we also obtain an achievable
rate for a fully quantum Gel'fand-Pinsker channel in the absence of Eve. The
form of this achievable rate matches with its classical counterpart. The
Gel'fand-Pinsker channel model had earlier only been studied for the
classical-quantum case and in the case where Alice (the sender) and Bob (the
receiver) have shared entanglement between them.Comment: version 2, 1 figure, 26 pages, added some extra proof and corrected
few typo