94 research outputs found
Source compression with a quantum helper
© 2015 IEEE. We study classical source coding with quantum side-information where the quantum side-information is observed by a helper and sent to the decoder via a classical channel. We derive a single-letter characterization of the achievable rate region for this problem. The direct part of our result is proved via the measurement compression theory by Winter. Our result reveals that a helper's scheme that separately conducts a measurement and a compression is suboptimal, and the measurement compression is fundamentally needed to achieve the optimal rate region
Fully quantum source compression with a quantum helper
© 2015 IEEE. We study source compression with a helper in the fully quantum regime, extending our earlier result on classical source compression with a quantum helper [arXiv:1501.04366, 2015]. We characterise the quantum resources involved in this problem, and derive a single-letter expression of the achievable rate region when entanglement assistance is available. The direct coding proof is based on a combination of two fundamental protocols, namely the quantum state merging protocol and the quantum reverse Shannon theorem (QRST). This result connects distributed source compression with the QRST protocol, a quantum protocol that consumes noiseless resources to simulate a noisy quantum channel
Lossless quantum data compression with exponential penalization: an operational interpretation of the quantum Rényi entropy
Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum Rényi entropies. In order to do this, we appeal to a very general quantum encoding scheme that satisfies a quantum version of the Kraft-McMillan inequality. Then, in the standard situation, where one is intended to minimize the usual average length of the quantum codewords, we recover the known results, namely that the von Neumann entropy of the source bounds the average length of the optimal codes. Otherwise, we show that by invoking an exponential average length, related to an exponential penalization over large codewords, the quantum Rényi entropies arise as the natural quantities relating the optimal encoding schemes with the source description, playing an analogous role to that of von Neumann entropy.Facultad de Ciencias Exacta
Gaussian Secure Source Coding and Wyner's Common Information
We study secure source-coding with causal disclosure, under the Gaussian
distribution. The optimality of Gaussian auxiliary random variables is shown in
various scenarios. We explicitly characterize the tradeoff between the rates of
communication and secret key. This tradeoff is the result of a mutual
information optimization under Markov constraints. As a corollary, we deduce a
general formula for Wyner's Common Information in the Gaussian setting.Comment: ISIT 2015, 5 pages, uses IEEEtran.cl
Causality, Information and Biological Computation: An algorithmic software approach to life, disease and the immune system
Biology has taken strong steps towards becoming a computer science aiming at
reprogramming nature after the realisation that nature herself has reprogrammed
organisms by harnessing the power of natural selection and the digital
prescriptive nature of replicating DNA. Here we further unpack ideas related to
computability, algorithmic information theory and software engineering, in the
context of the extent to which biology can be (re)programmed, and with how we
may go about doing so in a more systematic way with all the tools and concepts
offered by theoretical computer science in a translation exercise from
computing to molecular biology and back. These concepts provide a means to a
hierarchical organization thereby blurring previously clear-cut lines between
concepts like matter and life, or between tumour types that are otherwise taken
as different and may not have however a different cause. This does not diminish
the properties of life or make its components and functions less interesting.
On the contrary, this approach makes for a more encompassing and integrated
view of nature, one that subsumes observer and observed within the same system,
and can generate new perspectives and tools with which to view complex diseases
like cancer, approaching them afresh from a software-engineering viewpoint that
casts evolution in the role of programmer, cells as computing machines, DNA and
genes as instructions and computer programs, viruses as hacking devices, the
immune system as a software debugging tool, and diseases as an
information-theoretic battlefield where all these forces deploy. We show how
information theory and algorithmic programming may explain fundamental
mechanisms of life and death.Comment: 30 pages, 8 figures. Invited chapter contribution to Information and
Causality: From Matter to Life. Sara I. Walker, Paul C.W. Davies and George
Ellis (eds.), Cambridge University Pres
Distributed Channel Synthesis
Two familiar notions of correlation are rediscovered as the extreme operating
points for distributed synthesis of a discrete memoryless channel, in which a
stochastic channel output is generated based on a compressed description of the
channel input. Wyner's common information is the minimum description rate
needed. However, when common randomness independent of the input is available,
the necessary description rate reduces to Shannon's mutual information. This
work characterizes the optimal trade-off between the amount of common
randomness used and the required rate of description. We also include a number
of related derivations, including the effect of limited local randomness, rate
requirements for secrecy, applications to game theory, and new insights into
common information duality.
Our proof makes use of a soft covering lemma, known in the literature for its
role in quantifying the resolvability of a channel. The direct proof
(achievability) constructs a feasible joint distribution over all parts of the
system using a soft covering, from which the behavior of the encoder and
decoder is inferred, with no explicit reference to joint typicality or binning.
Of auxiliary interest, this work also generalizes and strengthens this soft
covering tool.Comment: To appear in IEEE Trans. on Information Theory (submitted Aug., 2012,
accepted July, 2013), 26 pages, using IEEEtran.cl
Lossless quantum data compression with exponential penalization: an operational interpretation of the quantum Rényi entropy
Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum Rényi entropies. In order to do this, we appeal to a very general quantum encoding scheme that satisfies a quantum version of the Kraft-McMillan inequality. Then, in the standard situation, where one is intended to minimize the usual average length of the quantum codewords, we recover the known results, namely that the von Neumann entropy of the source bounds the average length of the optimal codes. Otherwise, we show that by invoking an exponential average length, related to an exponential penalization over large codewords, the quantum Rényi entropies arise as the natural quantities relating the optimal encoding schemes with the source description, playing an analogous role to that of von Neumann entropy.Facultad de Ciencias Exacta
- …