21,204 research outputs found
Entangled inputs cannot make imperfect quantum channels perfect
Entangled inputs can enhance the capacity of quantum channels, this being one
of the consequences of the celebrated result showing the non-additivity of
several quantities relevant for quantum information science. In this work, we
answer the converse question (whether entangled inputs can ever render noisy
quantum channels have maximum capacity) to the negative: No sophisticated
entangled input of any quantum channel can ever enhance the capacity to the
maximum possible value; a result that holds true for all channels both for the
classical as well as the quantum capacity. This result can hence be seen as a
bound as to how "non-additive quantum information can be". As a main result, we
find first practical and remarkably simple computable single-shot bounds to
capacities, related to entanglement measures. As examples, we discuss the qubit
amplitude damping and identify the first meaningful bound for its classical
capacity.Comment: 5 pages, 2 figures, an error in the argument on the quantum capacity
corrected, version to be published in the Physical Review Letter
Time reversal and exchange symmetries of unitary gate capacities
Unitary gates are an interesting resource for quantum communication in part
because they are always invertible and are intrinsically bidirectional. This
paper explores these two symmetries: time-reversal and exchange of Alice and
Bob. We will present examples of unitary gates that exhibit dramatic
separations between forward and backward capacities (even when the back
communication is assisted by free entanglement) and between
entanglement-assisted and unassisted capacities, among many others. Along the
way, we will give a general time-reversal rule for relating the capacities of a
unitary gate and its inverse that will explain why previous attempts at finding
asymmetric capacities failed. Finally, we will see how the ability to erase
quantum information and destroy entanglement can be a valuable resource for
quantum communication.Comment: 17 pages. v2: improved bounds, clarified proofs. v3: published
version, added section explaining notatio
Tema Con Variazioni: Quantum Channel Capacity
Channel capacity describes the size of the nearly ideal channels, which can
be obtained from many uses of a given channel, using an optimal error
correcting code. In this paper we collect and compare minor and major
variations in the mathematically precise statements of this idea which have
been put forward in the literature. We show that all the variations considered
lead to equivalent capacity definitions. In particular, it makes no difference
whether one requires mean or maximal errors to go to zero, and it makes no
difference whether errors are required to vanish for any sequence of block
sizes compatible with the rate, or only for one infinite sequence.Comment: 32 pages, uses iopart.cl
Methods for Estimating Capacities and Rates of Gaussian Quantum Channels
Optimization methods aimed at estimating the capacities of a general Gaussian
channel are developed. Specifically evaluation of classical capacity as maximum
of the Holevo information is pursued over all possible Gaussian encodings for
the lossy bosonic channel, but extension to other capacities and other Gaussian
channels seems feasible. Solutions for both memoryless and memory channels are
presented. It is first dealt with single use (single-mode) channel where the
capacity dependence from channel's parameters is analyzed providing a full
classification of the possible cases. Then it is dealt with multiple uses
(multi-mode) channel where the capacity dependence from the (multi-mode)
environment state is analyzed when both total environment energy and
environment purity are fixed. This allows a fair comparison among different
environments, thus understanding the role of memory (inter-mode correlations)
and phenomenon like superadditivity of the capacity. The developed methods are
also used for deriving transmission rates with heterodyne and homodyne
measurements at the channel output. Classical capacity and transmission rates
are presented within a unique framework where the rates can be treated as
logarithmic approximations of the capacity.Comment: 39 pages, 30 figures. New results and graphs were added. Errors and
misprints were corrected. To appear in IEEE Trans. Inf. T
Quantum Channels with Memory
We present a general model for quantum channels with memory, and show that it
is sufficiently general to encompass all causal automata: any quantum process
in which outputs up to some time t do not depend on inputs at times t' > t can
be decomposed into a concatenated memory channel. We then examine and present
different physical setups in which channels with memory may be operated for the
transfer of (private) classical and quantum information. These include setups
in which either the receiver or a malicious third party have control of the
initializing memory. We introduce classical and quantum channel capacities for
these settings, and give several examples to show that they may or may not
coincide. Entropic upper bounds on the various channel capacities are given.
For forgetful quantum channels, in which the effect of the initializing memory
dies out as time increases, coding theorems are presented to show that these
bounds may be saturated. Forgetful quantum channels are shown to be open and
dense in the set of quantum memory channels.Comment: 21 pages with 5 EPS figures. V2: Presentation clarified, references
adde
Capacities of Grassmann channels
A new class of quantum channels called Grassmann channels is introduced and
their classical and quantum capacity is calculated. The channel class appears
in a study of the two-mode squeezing operator constructed from operators
satisfying the fermionic algebra. We compare Grassmann channels with the
channels induced by the bosonic two-mode squeezing operator. Among other
results, we challenge the relevance of calculating entanglement measures to
assess or compare the ability of bosonic and fermionic states to send quantum
information to uniformly accelerated frames.Comment: 33 pages, Accepted in Journal of Mathematical Physics; The role of
the (fermionic) braided tensor product for quantum Shannon theory, namely
capacity formulas, elucidated; The conclusion on the equivalence of Unruh
effect for bosons and fermions for quantum communication purposes made clear
and even more precis
Group transference techniques for the estimation of the decoherence times and capacities of quantum Markov semigroups
Capacities of quantum channels and decoherence times both quantify the extent
to which quantum information can withstand degradation by interactions with its
environment. However, calculating capacities directly is known to be
intractable in general. Much recent work has focused on upper bounding certain
capacities in terms of more tractable quantities such as specific norms from
operator theory. In the meantime, there has also been substantial recent
progress on estimating decoherence times with techniques from analysis and
geometry, even though many hard questions remain open. In this article, we
introduce a class of continuous-time quantum channels that we called
transferred channels, which are built through representation theory from a
classical Markov kernel defined on a compact group. We study two subclasses of
such kernels: H\"ormander systems on compact Lie-groups and Markov chains on
finite groups. Examples of transferred channels include the depolarizing
channel, the dephasing channel, and collective decoherence channels acting on
qubits. Some of the estimates presented are new, such as those for channels
that randomly swap subsystems. We then extend tools developed in earlier work
by Gao, Junge and LaRacuente to transfer estimates of the classical Markov
kernel to the transferred channels and study in this way different
non-commutative functional inequalities. The main contribution of this article
is the application of this transference principle to the estimation of various
capacities as well as estimation of entanglement breaking times, defined as the
first time for which the channel becomes entanglement breaking. Moreover, our
estimates hold for non-ergodic channels such as the collective decoherence
channels, an important scenario that has been overlooked so far because of a
lack of techniques.Comment: 35 pages, 2 figures. Close to published versio
Information gap for classical and quantum communication in a Schwarzschild spacetime
Communication between a free-falling observer and an observer hovering above
the Schwarzschild horizon of a black hole suffers from Unruh-Hawking noise,
which degrades communication channels. Ignoring time dilation, which affects
all channels equally, we show that for bosonic communication using single and
dual rail encoding the classical channel capacity reaches a finite value and
the quantum coherent information tends to zero. We conclude that classical
correlations still exist at infinite acceleration, whereas the quantum
coherence is fully removed.Comment: 5 pages, 4 figure
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