44,447 research outputs found
Network information theory for classical-quantum channels
Network information theory is the study of communication problems involving
multiple senders, multiple receivers and intermediate relay stations. The
purpose of this thesis is to extend the main ideas of classical network
information theory to the study of classical-quantum channels. We prove coding
theorems for quantum multiple access channels, quantum interference channels,
quantum broadcast channels and quantum relay channels.
A quantum model for a communication channel describes more accurately the
channel's ability to transmit information. By using physically faithful models
for the channel outputs and the detection procedure, we obtain better
communication rates than would be possible using a classical strategy. In this
thesis, we are interested in the transmission of classical information, so we
restrict our attention to the study of classical-quantum channels. These are
channels with classical inputs and quantum outputs, and so the coding theorems
we present will use classical encoding and quantum decoding. We study the
asymptotic regime where many copies of the channel are used in parallel, and
the uses are assumed to be independent. In this context, we can exploit
information-theoretic techniques to calculate the maximum rates for error-free
communication for any channel, given the statistics of the noise on that
channel. These theoretical bounds can be used as a benchmark to evaluate the
rates achieved by practical communication protocols.
Most of the results in this thesis consider classical-quantum channels with
finite dimensional output systems, which are analogous to classical discrete
memoryless channels. In the last chapter, we will show some applications of our
results to a practical optical communication scenario, in which the information
is encoded in continuous quantum degrees of freedom, which are analogous to
classical channels with Gaussian noise.Comment: Ph.D. Thesis, McGill University, School of Computer Science, July
2012, 223 pages, 18 figures, 36 TikZ diagram
Polar codes in network quantum information theory
Polar coding is a method for communication over noisy classical channels
which is provably capacity-achieving and has an efficient encoding and
decoding. Recently, this method has been generalized to the realm of quantum
information processing, for tasks such as classical communication, private
classical communication, and quantum communication. In the present work, we
apply the polar coding method to network quantum information theory, by making
use of recent advances for related classical tasks. In particular, we consider
problems such as the compound multiple access channel and the quantum
interference channel. The main result of our work is that it is possible to
achieve the best known inner bounds on the achievable rate regions for these
tasks, without requiring a so-called quantum simultaneous decoder. Thus, our
work paves the way for developing network quantum information theory further
without requiring a quantum simultaneous decoder.Comment: 18 pages, 2 figures, v2: 10 pages, double column, version accepted
for publicatio
Communication Enhancement Through Quantum Coherent Control of Channels in an Indefinite Causal-order Scenario
In quantum Shannon theory, transmission of information is enhanced by quantum
features. Up to very recently, the trajectories of transmission remained fully
classical. Recently, a new paradigm was proposed by playing quantum tricks on
two completely depolarizing quantum channels i.e. using coherent control in
space or time of the two quantum channels. We extend here this control to the
transmission of information through a network of an arbitrary number of
channels with arbitrary individual capacity i.e. information preservation
characteristics in the case of indefinite causal order. We propose a formalism
to assess information transmission in the most general case of channels in
an indefinite causal order scenario yielding the output of such transmission.
Then we explicitly derive the quantum switch output and the associated Holevo
limit of the information transmission for , as a function of all
involved parameters. We find in the case that the transmission of
information for three channels is twice of transmission of the two channel case
when a full superposition of all possible causal orders is used
Capacity Bounds for Quantum Communications through Quantum Trajectories
In both classical and quantum Shannon's information theory, communication
channels are generally assumed to combine through classical trajectories, so
that the associated network path traversed by the information carrier is
well-defined. Counter-intuitively, quantum mechanics enables a quantum
information carrier to propagate through a quantum trajectory, i.e., through a
path such that the causal order of the constituting communications channels
becomes indefinite. Quantum trajectories exhibit astonishing features, such as
providing non-null capacity even when no information can be sent through any
classical trajectory. But the fundamental question of investigating the
ultimate rates achievable with quantum trajectories is an open and crucial
problem. To this aim, in this paper, we derive closed-form expressions for both
the upper- and the lower-bound on the quantum capacity achievable via a quantum
trajectory. The derived expressions depend, remarkably, on computable
single-letter quantities. Our findings reveal the substantial advantage
achievable with a quantum trajectory over any classical combination of the
communications channels in terms of ultimate achievable communication rates.
Furthermore, we identify the region where a quantum trajectory incontrovertibly
outperforms the amount of transmissible information beyond the limits of
conventional quantum Shannon theory, and we quantify this advantage over
classical trajectories through a conservative estimate
Entropic descriptors of quantum communications in molecules
The classical Information Theory (IT) deals with entropic descriptors of the probability distributions and probability-propagation (communication) systems, e.g., the electronic channels in molecules reflecting the information scattering via the system chemical bonds. The quantum IT additionally accounts for the non-classical (current/phase)-related contributions in the resultant information content of electronic states. The classical and non-classical terms in the quantum Shannon entropy and Fisher information are reexamined. The associated probability-propagation and current-scattering networks are introduced and their Fisher- and Shannon-type descriptors are identified. The non-additive and additive information descriptors of the probability channels in both the Atomic Orbital and local resolution levels are related to the network conditional-entropy and mutual-information, which represent the IT covalency and ionicity components in the classical communication theory of the chemical bond. A similar partition identifies the associated bond indices in the molecular current/phase channels. The resultant bond descriptors combining the classical and non-classical terms, due to the probability and current distributions, respectively, are proposed as generalized communication-noise (covalency) and information-flow (iconicity) concepts in the quantum IT
Quantum information can be negative
Given an unknown quantum state distributed over two systems, we determine how
much quantum communication is needed to transfer the full state to one system.
This communication measures the "partial information" one system needs
conditioned on it's prior information. It turns out to be given by an extremely
simple formula, the conditional entropy. In the classical case, partial
information must always be positive, but we find that in the quantum world this
physical quantity can be negative. If the partial information is positive, its
sender needs to communicate this number of quantum bits to the receiver; if it
is negative, the sender and receiver instead gain the corresponding potential
for future quantum communication. We introduce a primitive "quantum state
merging" which optimally transfers partial information. We show how it enables
a systematic understanding of quantum network theory, and discuss several
important applications including distributed compression, multiple access
channels and multipartite assisted entanglement distillation (localizable
entanglement). Negative channel capacities also receive a natural
interpretation
Nonclassicality detection and communication bounds in quantum networks
Quantum information investigates the possibility of enhancing our ability to process and transmit information by directly exploiting quantum mechanical laws. When searching for improvement opportunities, one typically starts by assessing the range of outcomes classically attainable, and then investigates to what extent control over the quantum features of the system could be helpful, as well as the best performance that could be achieved. In this thesis we provide examples of these aspects, in linear optics, quantum metrology, and quantum communication.
We start by providing a criterion able to certify whether the outcome of a linear optical evolution cannot be explained by the classical wave-like theory of light. We do so by identifying a tight lower bound on the amount of correlations that could be detected among output intensities, when classical electrodynamics theory is used to describe the fields.
Rather than simply detecting nonclassicality, we then focus on its quantification. In particular, we consider the characterisation of the amount of squeezing encoded on selected quantum probes by an unknown external device, without prior information on the direction of application. We identify the single-mode Gaussian probes leading to the largest average precision in noiseless and noisy conditions, and discuss the advantages arising from the use of correlated two-mode probes.
Finally, we improve current bounds on the ultimate performance attainable in a quantum communication scenario. Specifically, we bound the number of maximally entangled qubits, or private bits, shared by two parties after a communication protocol over a quantum network, without restrictions on their classical communication. As in previous investigations, our approach is based on the evaluation of the maximum amount of entanglement that could be generated by the channels in the network, but it includes the possibility of changing entanglement measure on a channel-by-channel basis. Examples where this is advantageous are discussed.Open Acces
A Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
Achievability in information theory refers to demonstrating a coding strategy
that accomplishes a prescribed performance benchmark for the underlying task.
In quantum information theory, the crafted Hayashi-Nagaoka operator inequality
is an essential technique in proving a wealth of one-shot achievability bounds
since it effectively resembles a union bound in various problems. In this work,
we show that the pretty-good measurement naturally plays a role as the union
bound as well. A judicious application of it considerably simplifies the
derivation of one-shot achievability for classical-quantum (c-q) channel coding
via an elegant three-line proof.
The proposed analysis enjoys the following favorable features: (i) The
established one-shot bound admits a closed-form expression as in the celebrated
Holevo-Helstrom Theorem. Namely, the average error probability of sending
messages through a c-q channel is upper bounded by the error of distinguishing
the joint state between channel input and output against -many products
of its marginals. (ii) Our bound directly yields asymptotic results in the
large deviation, small deviation, and moderate deviation regimes in a unified
manner. (iii) The coefficients incurred in applying the Hayashi-Nagaoka
operator inequality are no longer needed. Hence, the derived one-shot bound
sharpens existing results that rely on the Hayashi-Nagaoka operator inequality.
In particular, we obtain the tightest achievable -one-shot capacity
for c-q channel heretofore, and it improves the third-order coding rate in the
asymptotic scenario. (iv) Our result holds for infinite-dimensional Hilbert
space. (v) The proposed method applies to deriving one-shot bounds for data
compression with quantum side information, entanglement-assisted classical
communication over quantum channels, and various quantum network
information-processing protocols
Secure Quantum Network Code without Classical Communication
We consider the secure quantum communication over a network with the presence
of a malicious adversary who can eavesdrop and contaminate the states. The
network consists of noiseless quantum channels with the unit capacity and the
nodes which applies noiseless quantum operations. As the main result, when the
maximum number m1 of the attacked channels over the entire network uses is less
than a half of the network transmission rate m0 (i.e., m1 < m0 / 2), our code
implements secret and correctable quantum communication of the rate m0 - 2m1 by
using the network asymptotic number of times. Our code is universal in the
sense that the code is constructed without the knowledge of the specific node
operations and the network topology, but instead, every node operation is
constrained to the application of an invertible matrix to the basis states.
Moreover, our code requires no classical communication. Our code can be thought
of as a generalization of the quantum secret sharing
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