Complete security proofs for quantum communication protocols can be
notoriously involved, which convolutes their verification, and obfuscates the
key physical insights the security finally relies on. In such cases, for the
majority of the community, the utility of such proofs may be restricted. Here
we provide a simple proof of confidentiality for parallel quantum channels
established via entanglement distillation based on hashing, in the presence of
noise, and a malicious eavesdropper who is restricted only by the laws of
quantum mechanics. The direct contribution lies in improving the linear
confidentiality levels of recurrence-type entanglement distillation protocols
to exponential levels for hashing protocols. The proof directly exploits the
security relevant physical properties: measurement-based quantum computation
with resource states and the separation of Bell-pairs from an eavesdropper. The
proof also holds for situations where Eve has full control over the input
states, and obtains all information about the operations and noise applied by
the parties. The resulting state after hashing is private, i.e., disentangled
from the eavesdropper. Moreover, the noise regimes for entanglement
distillation and confidentiality do not coincide: Confidentiality can be
guaranteed even in situation where entanglement distillation fails. We extend
our results to multiparty situations which are of special interest for secure
quantum networks.Comment: 5 + 11 pages, 0 + 4 figures, A. Pirker and M. Zwerger contributed
equally to this work, replaced with accepted versio
