5 research outputs found
A Quantum Multiparty Packing Lemma and the Relay Channel
Optimally encoding classical information in a quantum system is one of the
oldest and most fundamental challenges of quantum information theory. Holevo's
bound places a hard upper limit on such encodings, while the
Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many
classical messages can be "packed" into a given quantum system. In this
article, we use Sen's recent quantum joint typicality results to prove a
one-shot multiparty quantum packing lemma generalizing the HSW theorem. The
lemma is designed to be easily applicable in many network communication
scenarios. As an illustration, we use it to straightforwardly obtain quantum
generalizations of well-known classical coding schemes for the relay channel:
multihop, coherent multihop, decode-forward, and partial decode-forward. We
provide both finite blocklength and asymptotic results, the latter matching
existing classical formulas. Given the key role of the classical packing lemma
in network information theory, our packing lemma should help open the field to
direct quantum generalization.Comment: 20 page
Publicness, Privacy and Confidentiality in the Single-Serving Quantum Broadcast Channel
The 2-receiver broadcast channel is studied: a network with three parties
where the transmitter and one of the receivers are the primarily involved
parties and the other receiver considered as third party. The messages that are
determined to be communicated are classified into public, private and
confidential based on the information they convey. The public message contains
information intended for both parties and is required to be decoded correctly
by both of them, the private message is intended for the primary party only,
however, there is no secrecy requirement imposed upon it meaning that it can
possibly be exposed to the third party and finally the confidential message
containing information intended exclusively for the primary party such that
this information must be kept completely secret from the other receiver. A
trade-off arises between the rates of the three messages, when one of the rates
is high, the other rates may need to be reduced to guarantee the reliable
transmission of all three messages. The encoder performs the necessary
equivocation by virtue of dummy random numbers whose rate is assumed to be
limited and should be considered in the trade-off as well. We study this
trade-off in the one-shot regime of a quantum broadcast channel by providing
achievability and (weak) converse regions. In the achievability, we prove and
use a conditional version of the convex-split lemma as well as position-based
decoding. By studying the asymptotic behaviour of our bounds, we will recover
several well-known asymptotic results in the literature.Comment: 23 pages, 1 figure, journa
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