13,705 research outputs found
Polar codes for degradable quantum channels
Channel polarization is a phenomenon in which a particular recursive encoding
induces a set of synthesized channels from many instances of a memoryless
channel, such that a fraction of the synthesized channels becomes near perfect
for data transmission and the other fraction becomes near useless for this
task. Mahdavifar and Vardy have recently exploited this phenomenon to construct
codes that achieve the symmetric private capacity for private data transmission
over a degraded wiretap channel. In the current paper, we build on their work
and demonstrate how to construct quantum wiretap polar codes that achieve the
symmetric private capacity of a degraded quantum wiretap channel with a
classical eavesdropper. Due to the Schumacher-Westmoreland correspondence
between quantum privacy and quantum coherence, we can construct quantum polar
codes by operating these quantum wiretap polar codes in superposition, much
like Devetak's technique for demonstrating the achievability of the coherent
information rate for quantum data transmission. Our scheme achieves the
symmetric coherent information rate for quantum channels that are degradable
with a classical environment. This condition on the environment may seem
restrictive, but we show that many quantum channels satisfy this criterion,
including amplitude damping channels, photon-detected jump channels, dephasing
channels, erasure channels, and cloning channels. Our quantum polar coding
scheme has the desirable properties of being channel-adapted and symmetric
capacity-achieving along with having an efficient encoder, but we have not
demonstrated that the decoding is efficient. Also, the scheme may require
entanglement assistance, but we show that the rate of entanglement consumption
vanishes in the limit of large blocklength if the channel is degradable with
classical environment.Comment: 12 pages, 1 figure; v2: IEEE format, minor changes including new
figure; v3: minor changes, accepted for publication in IEEE Transactions on
Information Theor
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
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
Additive Extensions of a Quantum Channel
We study extensions of a quantum channel whose one-way capacities are
described by a single-letter formula. This provides a simple technique for
generating powerful upper bounds on the capacities of a general quantum
channel. We apply this technique to two qubit channels of particular
interest--the depolarizing channel and the channel with independent phase and
amplitude noise. Our study of the latter demonstrates that the key rate of BB84
with one-way post-processing and quantum bit error rate q cannot exceed
H(1/2-2q(1-q)) - H(2q(1-q)).Comment: 6 pages, one figur
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
Quantum Channel Capacities with Passive Environment Assistance
We initiate the study of passive environment-assisted communication via a
quantum channel, modeled as a unitary interaction between the information
carrying system and an environment. In this model, the environment is
controlled by a benevolent helper who can set its initial state such as to
assist sender and receiver of the communication link. (The case of a malicious
environment, also known as jammer, or arbitrarily varying channel, is
essentially well-understood and comprehensively reviewed.) Here, after setting
out precise definitions, focussing on the problem of quantum communication, we
show that entanglement plays a crucial role in this problem: indeed, the
assisted capacity where the helper is restricted to product states between
channel uses is different from the one with unrestricted helper. Furthermore,
prior shared entanglement between the helper and the receiver makes a
difference, too.Comment: 14 pages, 13 figures, IEEE format, Theorem 9 (statement and proof)
changed, updated References and Example 11 added. Comments are welcome
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