2,793 research outputs found
Strong converse theorems using R\'enyi entropies
We use a R\'enyi entropy method to prove strong converse theorems for certain
information-theoretic tasks which involve local operations and quantum or
classical communication between two parties. These include state
redistribution, coherent state merging, quantum state splitting, measurement
compression with quantum side information, randomness extraction against
quantum side information, and data compression with quantum side information.
The method we employ in proving these results extends ideas developed by Sharma
[arXiv:1404.5940], which he used to give a new proof of the strong converse
theorem for state merging. For state redistribution, we prove the strong
converse property for the boundary of the entire achievable rate region in the
-plane, where and denote the entanglement cost and quantum
communication cost, respectively. In the case of measurement compression with
quantum side information, we prove a strong converse theorem for the classical
communication cost, which is a new result extending the previously known weak
converse. For the remaining tasks, we provide new proofs for strong converse
theorems previously established using smooth entropies. For each task, we
obtain the strong converse theorem from explicit bounds on the figure of merit
of the task in terms of a R\'enyi generalization of the optimal rate. Hence, we
identify candidates for the strong converse exponents for each task discussed
in this paper. To prove our results, we establish various new entropic
inequalities, which might be of independent interest. These involve conditional
entropies and mutual information derived from the sandwiched R\'enyi
divergence. In particular, we obtain novel bounds relating these quantities, as
well as the R\'enyi conditional mutual information, to the fidelity of two
quantum states.Comment: 40 pages, 5 figures; v4: Accepted for publication in Journal of
Mathematical Physic
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
Information-theoretic aspects of the generalized amplitude damping channel
The generalized amplitude damping channel (GADC) is one of the sources of
noise in superconducting-circuit-based quantum computing. It can be viewed as
the qubit analogue of the bosonic thermal channel, and it thus can be used to
model lossy processes in the presence of background noise for low-temperature
systems. In this work, we provide an information-theoretic study of the GADC.
We first determine the parameter range for which the GADC is entanglement
breaking and the range for which it is anti-degradable. We then establish
several upper bounds on its classical, quantum, and private capacities. These
bounds are based on data-processing inequalities and the uniform continuity of
information-theoretic quantities, as well as other techniques. Our upper bounds
on the quantum capacity of the GADC are tighter than the known upper bound
reported recently in [Rosati et al., Nat. Commun. 9, 4339 (2018)] for the
entire parameter range of the GADC, thus reducing the gap between the lower and
upper bounds. We also establish upper bounds on the two-way assisted quantum
and private capacities of the GADC. These bounds are based on the squashed
entanglement, and they are established by constructing particular squashing
channels. We compare these bounds with the max-Rains information bound, the
mutual information bound, and another bound based on approximate covariance.
For all capacities considered, we find that a large variety of techniques are
useful in establishing bounds.Comment: 33 pages, 9 figures; close to the published versio
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