1,399 research outputs found
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
Quantum channels and their entropic characteristics
One of the major achievements of the recently emerged quantum information
theory is the introduction and thorough investigation of the notion of quantum
channel which is a basic building block of any data-transmitting or
data-processing system. This development resulted in an elaborated structural
theory and was accompanied by the discovery of a whole spectrum of entropic
quantities, notably the channel capacities, characterizing
information-processing performance of the channels. This paper gives a survey
of the main properties of quantum channels and of their entropic
characterization, with a variety of examples for finite dimensional quantum
systems. We also touch upon the "continuous-variables" case, which provides an
arena for quantum Gaussian systems. Most of the practical realizations of
quantum information processing were implemented in such systems, in particular
based on principles of quantum optics. Several important entropic quantities
are introduced and used to describe the basic channel capacity formulas. The
remarkable role of the specific quantum correlations - entanglement - as a
novel communication resource, is stressed.Comment: review article, 60 pages, 5 figures, 194 references; Rep. Prog. Phys.
(in press
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
The structure of degradable quantum channels
Degradable quantum channels are among the only channels whose quantum and
private classical capacities are known. As such, determining the structure of
these channels is a pressing open question in quantum information theory. We
give a comprehensive review of what is currently known about the structure of
degradable quantum channels, including a number of new results as well as
alternate proofs of some known results. In the case of qubits, we provide a
complete characterization of all degradable channels with two dimensional
output, give a new proof that a qubit channel with two Kraus operators is
either degradable or anti-degradable and present a complete description of
anti-degradable unital qubit channels with a new proof.
For higher output dimensions we explore the relationship between the output
and environment dimensions ( and respectively) of degradable
channels. For several broad classes of channels we show that they can be
modeled with a environment that is "small" in the sense . Perhaps
surprisingly, we also present examples of degradable channels with ``large''
environments, in the sense that the minimal dimension . Indeed, one
can have .
In the case of channels with diagonal Kraus operators, we describe the
subclass which are complements of entanglement breaking channels. We also
obtain a number of results for channels in the convex hull of conjugations with
generalized Pauli matrices. However, a number of open questions remain about
these channels and the more general case of random unitary channels.Comment: 42 pages, 3 figures, Web and paper abstract differ; (v2 contains only
minor typo corrections
The Private Classical Capacity of a Partially Degradable Quantum Channel
For a partially degradable (PD) channel, the channel output state can be used
to simulate the degraded environment state. The quantum capacity of a PD
channel has been proven to be additive. Here, we show that the private
classical capacity of arbitrary dimensional PD channels is equal to the quantum
capacity of the channel and also single-letterizes. We prove that higher rates
of private classical communication can be achieved over a PD channel in
comparison to standard degradable channels.Comment: 10 pages, Journal-ref: Physica Scripta, Special Issue on Quantum
Information (2014
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
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