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- Marco Tomamichel, Masahito Hayashi
- IEEE Transactions on Information Theory
- 2013

We consider two fundamental tasks in quantum information theory, data compression with quantum side information, as well as randomness extraction against quantum side information. We characterize these tasks for general sources using so-called one-shot entropies. These characterizations-in contrast to earlier results-enable us to derive tight second-order… (More)

The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi… (More)

The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi… (More)

- Marco Tomamichel, Roger Colbeck, Renato Renner
- IEEE Transactions on Information Theory
- 2010

In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two entropy measures, called smooth min-entropy and smooth max-entropy, respectively. While both entropies are equal to the von… (More)

- Masahito Hayashi, Marco Tomamichel
- ISIT
- 2015

Recently, a variety of new measures of quantum Rényi mutual information and quantum Rényi conditional entropy have been proposed, and some of their mathematical properties explored. Here, we show that the Rényi mutual information attains operational meaning in the context of composite hypothesis testing, when the null hypothesis is a fixed bipartite state… (More)

- Marco Tomamichel, Roger Colbeck, Renato Renner
- IEEE Transactions on Information Theory
- 2009

The classical asymptotic equipartition property is the statement that, in the limit of a large number of identical repetitions of a random experiment, the output sequence is virtually certain to come from the typical set, each member of which is almost equally likely. In this paper, a fully quantum generalization of this property is shown, where both the… (More)

- Marco Tomamichel, Charles Ci Wen Lim, Nicolas Gisin, Renato Renner
- Nature communications
- 2012

Despite enormous theoretical and experimental progress in quantum cryptography, the security of most current implementations of quantum key distribution is still not rigorously established. One significant problem is that the security of the final key strongly depends on the number, M, of signals exchanged between the legitimate parties. Yet, existing… (More)

- Marco Tomamichel, Vincent Yan Fu Tan
- IEEE Transactions on Information Theory
- 2013

This paper shows that the logarithm of the ε-error capacity (average error probability) for n uses of a discrete memoryless channel (DMC) is upper bounded by the normal approximation plus a third-order term that does not exceed [ 1/ 2] logn +O(1) if the ε-dispersion of the channel is positive. This matches a lower bound by Y. Polyanskiy (2010)… (More)

- Christopher T. Chubb, Vincent Y. F. Tan, Marco Tomamichel
- 2017 IEEE International Symposium on Information…
- 2017

We analyse families of codes for classical data transmission over quantum channels that have both a vanishing probability of error and a code rate approaching capacity as the code length increases. To characterise the fundamental tradeoff between decoding error, code rate and code length for such codes we introduce a quantum generalisation of the moderate… (More)

- Marco Tomamichel
- ArXiv
- 2015

Acknowledgements I was introduced to quantum information theory during my PhD studies in Renato Renner's group at ETH Zurich. It is from him that I learned most of what I know about quantum cryptography and smooth entropies. Renato also got me interested more generally in finite resource information theory as well as the entropies and other information… (More)