284 research outputs found
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
Explicit receivers for pure-interference bosonic multiple access channels
The pure-interference bosonic multiple access channel has two senders and one
receiver, such that the senders each communicate with multiple temporal modes
of a single spatial mode of light. The channel mixes the input modes from the
two users pairwise on a lossless beamsplitter, and the receiver has access to
one of the two output ports. In prior work, Yen and Shapiro found the capacity
region of this channel if encodings consist of coherent-state preparations.
Here, we demonstrate how to achieve the coherent-state Yen-Shapiro region (for
a range of parameters) using a sequential decoding strategy, and we show that
our strategy outperforms the rate regions achievable using conventional
receivers. Our receiver performs binary-outcome quantum measurements for every
codeword pair in the senders' codebooks. A crucial component of this scheme is
a non-destructive "vacuum-or-not" measurement that projects an n-symbol
modulated codeword onto the n-fold vacuum state or its orthogonal complement,
such that the post-measurement state is either the n-fold vacuum or has the
vacuum removed from the support of the n symbols' joint quantum state. This
receiver requires the additional ability to perform multimode optical
phase-space displacements which are realizable using a beamsplitter and a
laser.Comment: v1: 9 pages, 2 figures, submission to the 2012 International
Symposium on Information Theory and its Applications (ISITA 2012), Honolulu,
Hawaii, USA; v2: minor change
Quantum interference channels
The discrete memoryless interference channel is modelled as a conditional
probability distribution with two outputs depending on two inputs and has
widespread applications in practical communication scenarios. In this paper, we
introduce and study the quantum interference channel, a generalization of a
two-input, two-output memoryless channel to the setting of quantum Shannon
theory. We discuss three different coding strategies and obtain corresponding
achievable rate regions for quantum interference channels. We calculate the
capacity regions in the special cases of "very strong" and "strong"
interference. The achievability proof in the case of "strong" interference
exploits a novel quantum simultaneous decoder for two-sender quantum multiple
access channels. We formulate a conjecture regarding the existence of a quantum
simultaneous decoder in the three-sender case and use it to state the rates
achievable by a quantum Han-Kobayashi strategy.Comment: 10 pages, 2 figures, submitted to the 2011 Allerton Conference on
Communication, Control, and Computing; v3 has a proof for a two-sender
quantum simultaneous decoder and as a result, we get the capacity for
channels with strong interferenc
Classical communication over a quantum interference channel
Calculating the capacity of interference channels is a notorious open problem in classical information theory. Such channels have two senders and two receivers, and each sender would like to communicate with a partner receiver. The capacity of such channels is known exactly in the settings of very strong and strong interference, while the Han-Kobayashi coding strategy gives the best known achievable rate region in the general case. Here, we introduce and study the quantum interference channel, a natural generalization of the interference channel to the setting of quantum information theory. We restrict ourselves for the most part to channels with two classical inputs and two quantum outputs in order to simplify the presentation of our results (though generalizations of our results to channels with quantum inputs are straightforward). We are able to determine the exact classical capacity of this channel in the settings of very strong and strong interference, by exploiting Winter\u27s successive decoding strategy and a novel two-sender quantum simultaneous decoder, respectively. We provide a proof that a Han-Kobayashi strategy is achievable with Holevo information rates, up to a conjecture regarding the existence of a three-sender quantum simultaneous decoder. This conjecture holds for a special class of quantum multiple-access channels with average output states that commute, and we discuss some other variations of the conjecture that hold. Finally, we detail a connection between the quantum interference channel and prior work on the capacity of bipartite unitary gates. © 2012 IEEE
Sequential decoding of a general classical-quantum channel
Since a quantum measurement generally disturbs the state of a quantum system,
one might think that it should not be possible for a sender and receiver to
communicate reliably when the receiver performs a large number of sequential
measurements to determine the message of the sender. We show here that this
intuition is not true, by demonstrating that a sequential decoding strategy
works well even in the most general "one-shot" regime, where we are given a
single instance of a channel and wish to determine the maximal number of bits
that can be communicated up to a small failure probability. This result follows
by generalizing a non-commutative union bound to apply for a sequence of
general measurements. We also demonstrate two ways in which a receiver can
recover a state close to the original state after it has been decoded by a
sequence of measurements that each succeed with high probability. The second of
these methods will be useful in realizing an efficient decoder for fully
quantum polar codes, should a method ever be found to realize an efficient
decoder for classical-quantum polar codes.Comment: 12 pages; accepted for publication in the Proceedings of the Royal
Society
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
Sequential, successive, and simultaneous decoders for entanglement-assisted classical communication
Bennett et al. showed that allowing shared entanglement between a sender and
receiver before communication begins dramatically simplifies the theory of
quantum channels, and these results suggest that it would be worthwhile to
study other scenarios for entanglement-assisted classical communication. In
this vein, the present paper makes several contributions to the theory of
entanglement-assisted classical communication. First, we rephrase the
Giovannetti-Lloyd-Maccone sequential decoding argument as a more general
"packing lemma" and show that it gives an alternate way of achieving the
entanglement-assisted classical capacity. Next, we show that a similar
sequential decoder can achieve the Hsieh-Devetak-Winter region for
entanglement-assisted classical communication over a multiple access channel.
Third, we prove the existence of a quantum simultaneous decoder for
entanglement-assisted classical communication over a multiple access channel
with two senders. This result implies a solution of the quantum simultaneous
decoding conjecture for unassisted classical communication over quantum
multiple access channels with two senders, but the three-sender case still
remains open (Sen recently and independently solved this unassisted two-sender
case with a different technique). We then leverage this result to recover the
known regions for unassisted and assisted quantum communication over a quantum
multiple access channel, though our proof exploits a coherent quantum
simultaneous decoder. Finally, we determine an achievable rate region for
communication over an entanglement-assisted bosonic multiple access channel and
compare it with the Yen-Shapiro outer bound for unassisted communication over
the same channel.Comment: 33 pages, 2 figures; v2 contains a proof of the quantum simultaneous
decoding conjecture for two-sender quantum multiple access channels; v3 shows
how to recover the known unassisted and assisted quantum communication
regions with a coherent quantum simultaneous decode
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