21,273 research outputs found
The quantum capacity with symmetric side channels
We present an upper bound for the quantum channel capacity that is both
additive and convex. Our bound can be interpreted as the capacity of a channel
for high-fidelity quantum communication when assisted by a family of channels
that have no capacity on their own. This family of assistance channels, which
we call symmetric side channels, consists of all channels mapping symmetrically
to their output and environment. The bound seems to be quite tight, and for
degradable quantum channels it coincides with the unassisted channel capacity.
Using this symmetric side channel capacity, we find new upper bounds on the
capacity of the depolarizing channel. We also briefly indicate an analogous
notion for distilling entanglement using the same class of (one-way) channels,
yielding one of the few entanglement measures that is monotonic under local
operations with one-way classical communication (1-LOCC), but not under the
more general class of local operations with classical communication (LOCC).Comment: 10 pages, 4 figure
Public Quantum Communication and Superactivation
Is there a meaningful quantum counterpart to public communication? We argue
that the symmetric-side channel -- which distributes quantum information
symmetrically between the receiver and the environment -- is a good candidate
for a notion of public quantum communication in entanglement distillation and
quantum error correction.
This connection is partially motivated by [Brand\~ao and Oppenheim,
arXiv:1004.3328], where it was found that if a sender would like to communicate
a secret message to a receiver through an insecure quantum channel using a
shared quantum state as a key, then the insecure quantum channel is only ever
used to simulate a symmetric-side channel, and can always be replaced by it
without altering the optimal rate. Here we further show, in complete analogy to
the role of public classical communication, that assistance by a symmetric-side
channel makes equal the distillable entanglement, the recently-introduced
mutual independence, and a generalization of the latter, which quantifies the
extent to which one of the parties can perform quantum privacy amplification.
Symmetric-side channels, and the closely related erasure channel, have been
recently harnessed to provide examples of superactivation of the quantum
channel capacity. Our findings give new insight into this non-additivity of the
channel capacity and its relation to quantum privacy. In particular, we show
that single-copy superactivation protocols with the erasure channel, which
encompasses all examples of non-additivity of the quantum capacity found to
date, can be understood as a conversion of mutual independence into distillable
entanglement.Comment: 10 page
Game-theoretic characterization of antidegradable channels
We introduce a guessing game involving a quantum channel, three parties - the
sender, the receiver and an eavesdropper, Eve - and a quantum public side
channel. We prove that a necessary and sufficient condition for the quantum
channel to be antidegradable, is that Eve wins the game. We thus obtain a
complete operational characterization of antidegradable channels in a
game-theoretic framework.Comment: v2: published version, 14 pages, 1 figure; v1: 13 pages, 1 figur
Private Quantum Coding for Quantum Relay Networks
The relay encoder is an unreliable probabilistic device which is aimed at
helping the communication between the sender and the receiver. In this work we
show that in the quantum setting the probabilistic behavior can be completely
eliminated. We also show how to combine quantum polar encoding with
superactivation-assistance in order to achieve reliable and capacity-achieving
private communication over noisy quantum relay channels.Comment: 15 pages, 3 figures, Journal-ref: Lecture Notes in Computer Science,
Vol. 7479, pp. 239-250. Springer-Verlag, 2012, presented in part at the 11th
Intl. Conference on Quantum Communication, Measurement and Computing
(QCMC2012), v2: minor formatting change
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