28,334 research outputs found
The quantum dynamic capacity formula of a quantum channel
The dynamic capacity theorem characterizes the reliable communication rates
of a quantum channel when combined with the noiseless resources of classical
communication, quantum communication, and entanglement. In prior work, we
proved the converse part of this theorem by making contact with many previous
results in the quantum Shannon theory literature. In this work, we prove the
theorem with an "ab initio" approach, using only the most basic tools in the
quantum information theorist's toolkit: the Alicki-Fannes' inequality, the
chain rule for quantum mutual information, elementary properties of quantum
entropy, and the quantum data processing inequality. The result is a simplified
proof of the theorem that should be more accessible to those unfamiliar with
the quantum Shannon theory literature. We also demonstrate that the "quantum
dynamic capacity formula" characterizes the Pareto optimal trade-off surface
for the full dynamic capacity region. Additivity of this formula simplifies the
computation of the trade-off surface, and we prove that its additivity holds
for the quantum Hadamard channels and the quantum erasure channel. We then
determine exact expressions for and plot the dynamic capacity region of the
quantum dephasing channel, an example from the Hadamard class, and the quantum
erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections;
v3 has correction regarding the optimizatio
Trade-off coding for universal qudit cloners motivated by the Unruh effect
A "triple trade-off" capacity region of a noisy quantum channel provides a
more complete description of its capabilities than does a single capacity
formula. However, few full descriptions of a channel's ability have been given
due to the difficult nature of the calculation of such regions---it may demand
an optimization of information-theoretic quantities over an infinite number of
channel uses. This work analyzes the d-dimensional Unruh channel, a noisy
quantum channel which emerges in relativistic quantum information theory. We
show that this channel belongs to the class of quantum channels whose capacity
region requires an optimization over a single channel use, and as such is
tractable. We determine two triple-trade off regions, the quantum dynamic
capacity region and the private dynamic capacity region, of the d-dimensional
Unruh channel. Our results show that the set of achievable rate triples using
this coding strategy is larger than the set achieved using a time-sharing
strategy. Furthermore, we prove that the Unruh channel has a distinct structure
made up of universal qudit cloning channels, thus providing a clear
relationship between this relativistic channel and the process of stimulated
emission present in quantum optical amplifiers.Comment: 26 pages, 4 figures; v2 has minor corrections to Definition 2.
Definition 4 and Remark 5 have been adde
The pitfalls of deciding whether a quantum channel is (conjugate) degradable and how to avoid them
To decide whether a quantum channel is degradable is relatively easy: one has
to find at least one example of a degrading quantum channel. But in general, no
conclusive criterion exists to show the opposite. Using elementary methods we
derive a necessary and sufficient condition to decide under what circumstances
the conclusion is unambiguous. The findings lead to an extension of the
antidegradability region for qubit and qutrit transpose depolarizing channels.
In the qubit case we reproduce the known results for the class of qubit
depolarizing channels (due to their equivalence). One of the consequences is
that the optimal qubit and qutrit asymmetric cloners possess a single-letter
quantum capacity formula. We also investigate the ramifications of the
criterion for the search of exclusively conjugate degradable channels.Comment: v2: Full rank assumption added to the main theorem; to appear in Open
Systems & Information Dynamic
Entanglement-assisted private communication over quantum broadcast channels
We consider entanglement-assisted (EA) private communication over a quantum
broadcast channel, in which there is a single sender and multiple receivers. We
divide the receivers into two sets: the decoding set and the malicious set. The
decoding set and the malicious set can either be disjoint or can have a finite
intersection. For simplicity, we say that a single party Bob has access to the
decoding set and another party Eve has access to the malicious set, and both
Eve and Bob have access to the pre-shared entanglement with Alice. The goal of
the task is for Alice to communicate classical information reliably to Bob and
securely against Eve, and Bob can take advantage of pre-shared entanglement
with Alice. In this framework, we establish a lower bound on the one-shot EA
private capacity. When there exists a quantum channel mapping the state of the
decoding set to the state of the malicious set, such a broadcast channel is
said to be degraded. We establish an upper bound on the one-shot EA private
capacity in terms of smoothed min- and max-entropies for such channels. In the
limit of a large number of independent channel uses, we prove that the EA
private capacity of a degraded quantum broadcast channel is given by a
single-letter formula. Finally, we consider two specific examples of degraded
broadcast channels and find their capacities. In the first example, we consider
the scenario in which one part of Bob's laboratory is compromised by Eve. We
show that the capacity for this protocol is given by the conditional quantum
mutual information of a quantum broadcast channel, and so we thus provide an
operational interpretation to the dynamic counterpart of the conditional
quantum mutual information. In the second example, Eve and Bob have access to
mutually exclusive sets of outputs of a broadcast channel.Comment: v2: 23 pages, 2 figures, accepted for publication in the special
issue "Shannon's Information Theory 70 years on: applications in classical
and quantum physics" for Journal of Physics
Superadditivity in trade-off capacities of quantum channels
In this article, we investigate the additivity phenomenon in the dynamic
capacity of a quantum channel for trading classical communication, quantum
communication and entanglement. Understanding such additivity property is
important if we want to optimally use a quantum channel for general
communication purpose. However, in a lot of cases, the channel one will be
using only has an additive single or double resource capacity, and it is
largely unknown if this could lead to an superadditive double or triple
resource capacity. For example, if a channel has an additive classical and
quantum capacity, can the classical-quantum capacity be superadditive? In this
work, we answer such questions affirmatively.
We give proof-of-principle requirements for these channels to exist. In most
cases, we can provide an explicit construction of these quantum channels. The
existence of these superadditive phenomena is surprising in contrast to the
result that the additivity of both classical-entanglement and classical-quantum
capacity regions imply the additivity of the triple capacity region.Comment: 15 pages. v2: typo correcte
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