29 research outputs found
A father protocol for quantum broadcast channels
A new protocol for quantum broadcast channels based on the fully quantum
Slepian-Wolf protocol is presented. The protocol yields an achievable rate
region for entanglement-assisted transmission of quantum information through a
quantum broadcast channel that can be considered the quantum analogue of
Marton's region for classical broadcast channels. The protocol can be adapted
to yield achievable rate regions for unassisted quantum communication and for
entanglement-assisted classical communication; in the case of unassisted
transmission, the region we obtain has no independent constraint on the sum
rate, only on the individual transmission rates. Regularized versions of all
three rate regions are provably optimal.Comment: Typo in statement of Theorem 4 fixe
Unconstrained distillation capacities of a pure-loss bosonic broadcast channel
Bosonic channels are important in practice as they form a simple model for
free-space or fiber-optic communication. Here we consider a single-sender
two-receiver pure-loss bosonic broadcast channel and determine the
unconstrained capacity region for the distillation of bipartite entanglement
and secret key between the sender and each receiver, whenever they are allowed
arbitrary public classical communication. We show how the state merging
protocol leads to achievable rates in this setting, giving an inner bound on
the capacity region. We also evaluate an outer bound on the region by using the
relative entropy of entanglement and a `reduction by teleportation' technique.
The outer bounds match the inner bounds in the infinite-energy limit, thereby
establishing the unconstrained capacity region for such channels. Our result
could provide a useful benchmark for implementing a broadcasting of
entanglement and secret key through such channels. An important open question
relevant to practice is to determine the capacity region in both this setting
and the single-sender single-receiver case when there is an energy constraint
on the transmitter.Comment: v2: 6 pages, 3 figures, introduction revised, appendix added where
the result is extended to the 1-to-m pure-loss bosonic broadcast channel. v3:
minor revision, typo error correcte
A decoupling approach to classical data transmission over quantum channels
Most coding theorems in quantum Shannon theory can be proven using the
decoupling technique: to send data through a channel, one guarantees that the
environment gets no information about it; Uhlmann's theorem then ensures that
the receiver must be able to decode. While a wide range of problems can be
solved this way, one of the most basic coding problems remains impervious to a
direct application of this method: sending classical information through a
quantum channel. We will show that this problem can, in fact, be solved using
decoupling ideas, specifically by proving a "dequantizing" theorem, which
ensures that the environment is only classically correlated with the sent data.
Our techniques naturally yield a generalization of the
Holevo-Schumacher-Westmoreland Theorem to the one-shot scenario, where a
quantum channel can be applied only once
The apex of the family tree of protocols: Optimal rates and resource inequalities
We establish bounds on the maximum entanglement gain and minimum quantum
communication cost of the Fully Quantum Slepian-Wolf protocol in the one-shot
regime, which is considered to be at the apex of the existing family tree in
Quantum Information Theory. These quantities, which are expressed in terms of
smooth min- and max-entropies, reduce to the known rates of quantum
communication cost and entanglement gain in the asymptotic i.i.d. scenario. We
also provide an explicit proof of the optimality of these asymptotic rates. We
introduce a resource inequality for the one-shot FQSW protocol, which in
conjunction with our results, yields achievable one-shot rates of its children
protocols. In particular, it yields bounds on the one-shot quantum capacity of
a noisy channel in terms of a single entropic quantity, unlike previously
bounds. We also obtain an explicit expression for the achievable rate for
one-shot state redistribution.Comment: 31 pages, 2 figures. Published versio
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
Classical codes for quantum broadcast channels
We discuss two techniques for transmitting classical information over quantum broadcast channels. The first technique is a quantum generalization of the superposition coding scheme for the classical broadcast channel. We use a quantum simultaneous nonunique decoder and obtain a simpler proof of the rate region recently published by Yard et al. in independent work. Our second result is a quantum Marton coding scheme, which gives the best known achievable rate region for quantum broadcast channels. Both results exploit recent advances in quantum simultaneous decoding developed in the context of quantum interference channels. © 2012 IEEE