360 research outputs found
Secure communication over fully quantum Gel'fand-Pinsker wiretap channel
In this work we study the problem of secure communication over a fully
quantum Gel'fand-Pinsker channel. The best known achievability rate for this
channel model in the classical case was proven by Goldfeld, Cuff and Permuter
in [Goldfeld, Cuff, Permuter, 2016]. We generalize the result of [Goldfeld,
Cuff, Permuter, 2016]. One key feature of the results obtained in this work is
that all the bounds obtained are in terms of error exponent. We obtain our
achievability result via the technique of simultaneous pinching. This in turn
allows us to show the existence of a simultaneous decoder. Further, to obtain
our encoding technique and to prove the security feature of our coding scheme
we prove a bivariate classical-quantum channel resolvability lemma and a
conditional classical-quantum channel resolvability lemma. As a by product of
the achievability result obtained in this work, we also obtain an achievable
rate for a fully quantum Gel'fand-Pinsker channel in the absence of Eve. The
form of this achievable rate matches with its classical counterpart. The
Gel'fand-Pinsker channel model had earlier only been studied for the
classical-quantum case and in the case where Alice (the sender) and Bob (the
receiver) have shared entanglement between them.Comment: version 2, 1 figure, 26 pages, added some extra proof and corrected
few typo
Converse bounds for private communication over quantum channels
This paper establishes several converse bounds on the private transmission
capabilities of a quantum channel. The main conceptual development builds
firmly on the notion of a private state, which is a powerful, uniquely quantum
method for simplifying the tripartite picture of privacy involving local
operations and public classical communication to a bipartite picture of quantum
privacy involving local operations and classical communication. This approach
has previously led to some of the strongest upper bounds on secret key rates,
including the squashed entanglement and the relative entropy of entanglement.
Here we use this approach along with a "privacy test" to establish a general
meta-converse bound for private communication, which has a number of
applications. The meta-converse allows for proving that any quantum channel's
relative entropy of entanglement is a strong converse rate for private
communication. For covariant channels, the meta-converse also leads to
second-order expansions of relative entropy of entanglement bounds for private
communication rates. For such channels, the bounds also apply to the private
communication setting in which the sender and receiver are assisted by
unlimited public classical communication, and as such, they are relevant for
establishing various converse bounds for quantum key distribution protocols
conducted over these channels. We find precise characterizations for several
channels of interest and apply the methods to establish several converse bounds
on the private transmission capabilities of all phase-insensitive bosonic
channels.Comment: v3: 53 pages, 3 figures, final version accepted for publication in
IEEE Transactions on Information Theor
Understanding interdependency through complex information sharing
The interactions between three or more random variables are often nontrivial,
poorly understood, and yet, are paramount for future advances in fields such as
network information theory, neuroscience, genetics and many others. In this
work, we propose to analyze these interactions as different modes of
information sharing. Towards this end, we introduce a novel axiomatic framework
for decomposing the joint entropy, which characterizes the various ways in
which random variables can share information. The key contribution of our
framework is to distinguish between interdependencies where the information is
shared redundantly, and synergistic interdependencies where the sharing
structure exists in the whole but not between the parts. We show that our
axioms determine unique formulas for all the terms of the proposed
decomposition for a number of cases of interest. Moreover, we show how these
results can be applied to several network information theory problems,
providing a more intuitive understanding of their fundamental limits.Comment: 39 pages, 4 figure
Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
A bipartite quantum interaction corresponds to the most general quantum
interaction that can occur between two quantum systems in the presence of a
bath. In this work, we determine bounds on the capacities of bipartite
interactions for entanglement generation and secret key agreement between two
quantum systems. Our upper bound on the entanglement generation capacity of a
bipartite quantum interaction is given by a quantity called the bidirectional
max-Rains information. Our upper bound on the secret-key-agreement capacity of
a bipartite quantum interaction is given by a related quantity called the
bidirectional max-relative entropy of entanglement. We also derive tighter
upper bounds on the capacities of bipartite interactions obeying certain
symmetries. Observing that reading of a memory device is a particular kind of
bipartite quantum interaction, we leverage our bounds from the bidirectional
setting to deliver bounds on the capacity of a task that we introduce, called
private reading of a wiretap memory cell. Given a set of point-to-point quantum
wiretap channels, the goal of private reading is for an encoder to form
codewords from these channels, in order to establish secret key with a party
who controls one input and one output of the channels, while a passive
eavesdropper has access to one output of the channels. We derive both lower and
upper bounds on the private reading capacities of a wiretap memory cell. We
then extend these results to determine achievable rates for the generation of
entanglement between two distant parties who have coherent access to a
controlled point-to-point channel, which is a particular kind of bipartite
interaction.Comment: v3: 34 pages, 3 figures, accepted for publication in Physical Review
Wiretap and Gelfand-Pinsker Channels Analogy and its Applications
An analogy framework between wiretap channels (WTCs) and state-dependent
point-to-point channels with non-causal encoder channel state information
(referred to as Gelfand-Pinker channels (GPCs)) is proposed. A good sequence of
stealth-wiretap codes is shown to induce a good sequence of codes for a
corresponding GPC. Consequently, the framework enables exploiting existing
results for GPCs to produce converse proofs for their wiretap analogs. The
analogy readily extends to multiuser broadcasting scenarios, encompassing
broadcast channels (BCs) with deterministic components, degradation ordering
between users, and BCs with cooperative receivers. Given a wiretap BC (WTBC)
with two receivers and one eavesdropper, an analogous Gelfand-Pinsker BC (GPBC)
is constructed by converting the eavesdropper's observation sequence into a
state sequence with an appropriate product distribution (induced by the
stealth-wiretap code for the WTBC), and non-causally revealing the states to
the encoder. The transition matrix of the state-dependent GPBC is extracted
from WTBC's transition law, with the eavesdropper's output playing the role of
the channel state. Past capacity results for the semi-deterministic (SD) GPBC
and the physically-degraded (PD) GPBC with an informed receiver are leveraged
to furnish analogy-based converse proofs for the analogous WTBC setups. This
characterizes the secrecy-capacity regions of the SD-WTBC and the PD-WTBC, in
which the stronger receiver also observes the eavesdropper's channel output.
These derivations exemplify how the wiretap-GP analogy enables translating
results on one problem into advances in the study of the other
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