3,848 research outputs found
Factor Graphs for Quantum Information Processing
[...] In this thesis, we are interested in generalizing factor graphs and the
relevant methods toward describing quantum systems. Two generalizations of
classical graphical models are investigated, namely double-edge factor graphs
(DeFGs) and quantum factor graphs (QFGs). Conventionally, a factor in a factor
graph represents a nonnegative real-valued local functions. Two different
approaches to generalize factors in classical factor graphs yield DeFGs and
QFGs, respectively. We proposed/re-proposed and analyzed generalized versions
of belief-propagation algorithms for DeFGs/QFGs. As a particular application of
the DeFGs, we investigate the information rate and their upper/lower bounds of
classical communications over quantum channels with memory. In this study, we
also propose a data-driven method for optimizing the upper/lower bounds on
information rate.Comment: This is the finial version of the thesis of Michael X. Cao submitted
in April 2021 in partial fulfillment of the requirements for the degree of
doctor of philosophy in information engineering at the Chinese university of
Hong Kon
Bounding and Estimating the Classical Information Rate of Quantum Channels with Memory
We consider the scenario of classical communication over a finite-dimensional
quantum channel with memory using a separable-state input ensemble and local
output measurements. We propose algorithms for estimating the information rate
of such communication setups, along with algorithms for bounding the
information rate based on so-called auxiliary channels. Some of the algorithms
are extensions of their counterparts for (classical) finite-state-machine
channels. Notably, we discuss suitable graphical models for doing the relevant
computations. Moreover, the auxiliary channels are learned in a data-driven
approach; i.e., only input/output sequences of the true channel are needed, but
not the channel model of the true channel.Comment: This work has been submitted to the IEEE Transactions on Information
Theory for possible publication. Copyright may be transferred without notice,
after which this version may no longer be accessibl
A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels
We use the smooth entropy approach to treat the problems of binary quantum
hypothesis testing and the transmission of classical information through a
quantum channel. We provide lower and upper bounds on the optimal type II error
of quantum hypothesis testing in terms of the smooth max-relative entropy of
the two states representing the two hypotheses. Using then a relative entropy
version of the Quantum Asymptotic Equipartition Property (QAEP), we can recover
the strong converse rate of the i.i.d. hypothesis testing problem in the
asymptotics. On the other hand, combining Stein's lemma with our bounds, we
obtain a stronger (\ep-independent) version of the relative entropy-QAEP.
Similarly, we provide bounds on the one-shot \ep-error classical capacity of
a quantum channel in terms of a smooth max-relative entropy variant of its
Holevo capacity. Using these bounds and the \ep-independent version of the
relative entropy-QAEP, we can recover both the Holevo-Schumacher-Westmoreland
theorem about the optimal direct rate of a memoryless quantum channel with
product state encoding, as well as its strong converse counterpart.Comment: v4: Title changed, improved bounds, both direct and strong converse
rates are covered, a new Discussion section added. 20 page
Information transmission over an amplitude damping channel with an arbitrary degree of memory
We study the performance of a partially correlated amplitude damping channel
acting on two qubits. We derive lower bounds for the single-shot classical
capacity by studying two kinds of quantum ensembles, one which allows to
maximize the Holevo quantity for the memoryless channel and the other allowing
the same task but for the full-memory channel. In these two cases, we also show
the amount of entanglement which is involved in achieving the maximum of the
Holevo quantity. For the single-shot quantum capacity we discuss both a lower
and an upper bound, achieving a good estimate for high values of the channel
transmissivity. We finally compute the entanglement-assisted classical channel
capacity.Comment: 17 pages, 7 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
Quantum reading capacity: General definition and bounds
Quantum reading refers to the task of reading out classical information
stored in a read-only memory device. In any such protocol, the transmitter and
receiver are in the same physical location, and the goal of such a protocol is
to use these devices (modeled by independent quantum channels), coupled with a
quantum strategy, to read out as much information as possible from a memory
device, such as a CD or DVD. As a consequence of the physical setup of quantum
reading, the most natural and general definition for quantum reading capacity
should allow for an adaptive operation after each call to the channel, and this
is how we define quantum reading capacity in this paper. We also establish
several bounds on quantum reading capacity, and we introduce an
environment-parametrized memory cell with associated environment states,
delivering second-order and strong converse bounds for its quantum reading
capacity. We calculate the quantum reading capacities for some exemplary memory
cells, including a thermal memory cell, a qudit erasure memory cell, and a
qudit depolarizing memory cell. We finally provide an explicit example to
illustrate the advantage of using an adaptive strategy in the context of
zero-error quantum reading capacity.Comment: v3: 17 pages, 2 figures, final version published in IEEE Transactions
on Information Theor
Fundamental rate-loss tradeoff for optical quantum key distribution
Since 1984, various optical quantum key distribution (QKD) protocols have
been proposed and examined. In all of them, the rate of secret key generation
decays exponentially with distance. A natural and fundamental question is then
whether there are yet-to-be discovered optical QKD protocols (without quantum
repeaters) that could circumvent this rate-distance tradeoff. This paper
provides a major step towards answering this question. We show that the
secret-key-agreement capacity of a lossy and noisy optical channel assisted by
unlimited two-way public classical communication is limited by an upper bound
that is solely a function of the channel loss, regardless of how much optical
power the protocol may use. Our result has major implications for understanding
the secret-key-agreement capacity of optical channels---a long-standing open
problem in optical quantum information theory---and strongly suggests a real
need for quantum repeaters to perform QKD at high rates over long distances.Comment: 9+4 pages, 3 figures. arXiv admin note: text overlap with
arXiv:1310.012
- …