7 research outputs found
Quantum intersection and union
In information theory, we often use intersection and union of the typical
sets to analyze various communication problems. However, in the quantum setting
it is not very clear how to construct a measurement which behaves analogous to
intersection and union of the typical sets. In this work, we construct a
projection operator which behaves very similar to intersection and union of the
typical sets. Our construction relies on the Jordan's lemma. Using this
construction we study the problem of communication over authenticated
classical-quantum channels and derive its capacity. As another application of
our construction, we study the problem of quantum asymmetric composite
hypothesis testing. Further, we also prove a converse for the quantum binary
asymmetric hypothesis testing problem which is arguably very similar in spirit
to the converse given in the Thomas and Cover book for the classical version of
this problem
Byzantine Multiple Access Channels -- Part II: Communication With Adversary Identification
We introduce the problem of determining the identity of a byzantine user
(internal adversary) in a communication system. We consider a two-user discrete
memoryless multiple access channel where either user may deviate from the
prescribed behaviour. Owing to the noisy nature of the channel, it may be
overly restrictive to attempt to detect all deviations. In our formulation, we
only require detecting deviations which impede the decoding of the
non-deviating user's message. When neither user deviates, correct decoding is
required. When one user deviates, the decoder must either output a pair of
messages of which the message of the non-deviating user is correct or identify
the deviating user. The users and the receiver do not share any randomness. The
results include a characterization of the set of channels where communication
is feasible, and an inner and outer bound on the capacity region. We also show
that whenever the rate region has non-empty interior, the capacity region is
same as the capacity region under randomized encoding, where each user shares
independent randomness with the receiver. We also give an outer bound for this
randomized coding capacity region.Comment: arXiv admin note: substantial text overlap with arXiv:2105.0338