518 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
Quantum Information Transmission over a Partially Degradable Channel
We investigate a quantum coding for quantum communication over a PD
(partially degradable) degradable quantum channel. For a PD channel, the
degraded environment state can be expressed from the channel output state up to
a degrading map. PD channels can be restricted to the set of optical channels
which allows for the parties to exploit the benefits in experimental quantum
communications. We show that for a PD channel, the partial degradability
property leads to higher quantum data rates in comparison to those of a
degradable channel. The PD property is particular convenient for quantum
communications and allows one to implement the experimental quantum protocols
with higher performance. We define a coding scheme for PD-channels and give the
achievable rates of quantum communication.Comment: 7 pages, 2 figures, Journal-ref: IEEE Acces
Polar codes for private classical communication
We construct a new secret-key assisted polar coding scheme for private
classical communication over a quantum or classical wiretap channel. The
security of our scheme rests on an entropic uncertainty relation, in addition
to the channel polarization effect. Our scheme achieves the symmetric private
information rate by synthesizing "amplitude" and "phase" channels from an
arbitrary quantum wiretap channel. We find that the secret-key consumption rate
of the scheme vanishes for an arbitrary degradable quantum wiretap channel.
Furthermore, we provide an additional sufficient condition for when the secret
key rate vanishes, and we suspect that satisfying this condition implies that
the scheme requires no secret key at all. Thus, this latter condition addresses
an open question from the Mahdavifar-Vardy scheme for polar coding over a
classical wiretap channel.Comment: 11 pages, 2 figures, submission to the 2012 International Symposium
on Information Theory and its Applications (ISITA 2012), Honolulu, Hawaii,
US
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
Magic state distillation with punctured polar codes
We present a scheme for magic state distillation using punctured polar codes.
Our results build on some recent work by Bardet et al. (ISIT, 2016) who
discovered that polar codes can be described algebraically as decreasing
monomial codes. Using this powerful framework, we construct tri-orthogonal
quantum codes (Bravyi et al., PRA, 2012) that can be used to distill magic
states for the gate. An advantage of these codes is that they permit the
use of the successive cancellation decoder whose time complexity scales as
. We supplement this with numerical simulations for the erasure
channel and dephasing channel. We obtain estimates for the dimensions and error
rates for the resulting codes for block sizes up to for the erasure
channel and for the dephasing channel. The dimension of the
triply-even codes we obtain is shown to scale like for the binary
erasure channel at noise rate and for the dephasing
channel at noise rate . The corresponding bit error rates drop to
roughly for the erasure channel and for
the dephasing channel respectively.Comment: 18 pages, 4 figure
An improved rate region for the classical-quantum broadcast channel
We present a new achievable rate region for the two-user binary-input
classical-quantum broadcast channel. The result is a generalization of the
classical Marton-Gelfand-Pinsker region and is provably larger than the best
previously known rate region for classical-quantum broadcast channels. The
proof of achievability is based on the recently introduced polar coding scheme
and its generalization to quantum network information theory.Comment: 5 pages, double column, 1 figure, based on a result presented in the
Master's thesis arXiv:1501.0373
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