2,879 research outputs found
Coding Theorems of Quantum Information Theory
Coding theorems and (strong) converses for memoryless quantum communication
channels and quantum sources are proved: for the quantum source the coding
theorem is reviewed, and the strong converse proven. For classical information
transmission via quantum channels we give a new proof of the coding theorem,
and prove the strong converse, even under the extended model of nonstationary
channels. As a by-product we obtain a new proof of the famous Holevo bound.
Then multi-user systems are investigated, and the capacity region for the
quantum multiple access channel is determined. The last chapter contains a
preliminary discussion of some models of compression of correlated quantum
sources, and a proposal for a program to obtain operational meaning for quantum
conditional entropy. An appendix features the introduction of a notation and
calculus of entropy in quantum systems.Comment: 80 pages, Ph.D. dissertation, Uni Bielefel
A Fundamental Inequality for Lower-bounding the Error Probability for Classical and Quantum Multiple Access Channels and Its Applications
In the study of the capacity problem for multiple access channels (MACs), a
lower bound on the error probability obtained by Han plays a crucial role in
the converse parts of several kinds of channel coding theorems in the
information-spectrum framework. Recently, Yagi and Oohama showed a tighter
bound than the Han bound by means of Polyanskiy's converse. In this paper, we
give a new bound which generalizes and strengthens the Yagi-Oohama bound, and
demonstrate that the bound plays a fundamental role in deriving extensions of
several known bounds. In particular, the Yagi-Oohama bound is generalized to
two different directions; i.e, to general input distributions and to general
encoders. In addition we extend these bounds to the quantum MACs and apply them
to the converse problems for several information-spectrum settings.Comment: under submissio
Strong converse for the classical capacity of optical quantum communication channels
We establish the classical capacity of optical quantum channels as a sharp
transition between two regimes---one which is an error-free regime for
communication rates below the capacity, and the other in which the probability
of correctly decoding a classical message converges exponentially fast to zero
if the communication rate exceeds the classical capacity. This result is
obtained by proving a strong converse theorem for the classical capacity of all
phase-insensitive bosonic Gaussian channels, a well-established model of
optical quantum communication channels, such as lossy optical fibers, amplifier
and free-space communication. The theorem holds under a particular
photon-number occupation constraint, which we describe in detail in the paper.
Our result bolsters the understanding of the classical capacity of these
channels and opens the path to applications, such as proving the security of
noisy quantum storage models of cryptography with optical links.Comment: 15 pages, final version accepted into IEEE Transactions on
Information Theory. arXiv admin note: text overlap with arXiv:1312.328
Strong converse rates for classical communication over thermal and additive noise bosonic channels
We prove that several known upper bounds on the classical capacity of thermal
and additive noise bosonic channels are actually strong converse rates. Our
results strengthen the interpretation of these upper bounds, in the sense that
we now know that the probability of correctly decoding a classical message
rapidly converges to zero in the limit of many channel uses if the
communication rate exceeds these upper bounds. In order for these theorems to
hold, we need to impose a maximum photon number constraint on the states input
to the channel (the strong converse property need not hold if there is only a
mean photon number constraint). Our first theorem demonstrates that Koenig and
Smith's upper bound on the classical capacity of the thermal bosonic channel is
a strong converse rate, and we prove this result by utilizing the structural
decomposition of a thermal channel into a pure-loss channel followed by an
amplifier channel. Our second theorem demonstrates that Giovannetti et al.'s
upper bound on the classical capacity of a thermal bosonic channel corresponds
to a strong converse rate, and we prove this result by relating success
probability to rate, the effective dimension of the output space, and the
purity of the channel as measured by the Renyi collision entropy. Finally, we
use similar techniques to prove that similar previously known upper bounds on
the classical capacity of an additive noise bosonic channel correspond to
strong converse rates.Comment: Accepted for publication in Physical Review A; minor changes in the
text and few reference
The Capacity of the Quantum Multiple Access Channel
We define classical-quantum multiway channels for transmission of classical
information, after recent work by Allahverdyan and Saakian. Bounds on the
capacity region are derived in a uniform way, which are analogous to the
classically known ones, simply replacing Shannon entropy with von Neumann
entropy. For the single receiver case (multiple access channel) the exact
capacity region is determined. These results are applied to the case of noisy
channels, with arbitrary input signal states. A second issue of this work is
the presentation of a calculus of quantum information quantities, based on the
algebraic formulation of quantum theory.Comment: 7 pages, requires IEEEtran2e.cl
Strong converse rates for quantum communication
We revisit a fundamental open problem in quantum information theory, namely
whether it is possible to transmit quantum information at a rate exceeding the
channel capacity if we allow for a non-vanishing probability of decoding error.
Here we establish that the Rains information of any quantum channel is a strong
converse rate for quantum communication: For any sequence of codes with rate
exceeding the Rains information of the channel, we show that the fidelity
vanishes exponentially fast as the number of channel uses increases. This
remains true even if we consider codes that perform classical post-processing
on the transmitted quantum data. As an application of this result, for
generalized dephasing channels we show that the Rains information is also
achievable, and thereby establish the strong converse property for quantum
communication over such channels. Thus we conclusively settle the strong
converse question for a class of quantum channels that have a non-trivial
quantum capacity.Comment: v4: 13 pages, accepted for publication in IEEE Transactions on
Information Theor
Classical capacity of bosonic broadcast communication and a new minimum output entropy conjecture
Previous work on the classical information capacities of bosonic channels has
established the capacity of the single-user pure-loss channel, bounded the
capacity of the single-user thermal-noise channel, and bounded the capacity
region of the multiple-access channel. The latter is a multi-user scenario in
which several transmitters seek to simultaneously and independently communicate
to a single receiver. We study the capacity region of the bosonic broadcast
channel, in which a single transmitter seeks to simultaneously and
independently communicate to two different receivers. It is known that the
tightest available lower bound on the capacity of the single-user thermal-noise
channel is that channel's capacity if, as conjectured, the minimum von Neumann
entropy at the output of a bosonic channel with additive thermal noise occurs
for coherent-state inputs. Evidence in support of this minimum output entropy
conjecture has been accumulated, but a rigorous proof has not been obtained. In
this paper, we propose a new minimum output entropy conjecture that, if proved
to be correct, will establish that the capacity region of the bosonic broadcast
channel equals the inner bound achieved using a coherent-state encoding and
optimum detection. We provide some evidence that supports this new conjecture,
but again a full proof is not available.Comment: 13 pages, 7 figure
Capacity Theorems for Quantum Multiple Access Channels
We consider quantum channels with two senders and one receiver. For an
arbitrary such channel, we give multi-letter characterizations of two different
two-dimensional capacity regions. The first region characterizes the rates at
which it is possible for one sender to send classical information while the
other sends quantum information. The second region gives the rates at which
each sender can send quantum information. We give an example of a channel for
which each region has a single-letter description, concluding with a
characterization of the rates at which each user can simultaneously send
classical and quantum information.Comment: 5 pages. Conference version of quant-ph/0501045, to appear in the
proceedings of the IEEE International Symposium on Information Theory,
Adelaide, Australia, 200
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