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Martin Müller-Lennert,1 Frédéric Dupuis,2 Oleg Szehr,3 Serge Fehr,4 and Marco Tomamichel5 Department of Mathematics, ETH Zurich, 8092 Zürich, Switzerland Department of Computer Science, Aarhus University, 8200 Aarhus, Denmark Department of Mathematics, Technische Universität München, 85748 Garching, Germany CWI (Centrum Wiskunde & Informatica), 1090… (More)

- 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)

- Marco Tomamichel, Renato Renner, Christian Schaffner, Adam D. Smith
- IEEE Transactions on Information Theory
- 2010

The Leftover Hash Lemma states that the output of a two-universal hash function applied to an input with sufficiently high entropy is almost uniformly random. In its standard formulation, the lemma refers to a notion of randomness that is (usually implicitly) defined with respect to classical side information. Here, a strictly more general version of the… (More)

Martin Müller-Lennert,1 Frédéric Dupuis,2 Oleg Szehr,3 Serge Fehr,4 and Marco Tomamichel5 Department of Mathematics, ETH Zurich, 8092 Zürich, Switzerland Department of Computer Science, Aarhus University, 8200 Aarhus, Denmark Department of Mathematics, Technische Universität München, 85748 Garching, Germany CWI (Centrum Wiskunde & Informatica), 1090… (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)

- Marco Tomamichel, Renato Renner
- Physical review letters
- 2011

Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data (e.g., a description of the system's state before measurement), an extended relation which remains valid in the… (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, 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)

- 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)

- Vincent Yan Fu Tan, Marco Tomamichel
- IEEE Transactions on Information Theory
- 2014

This paper shows that, under the average error probability formalism, the third-order term in the normal approximation for the additive white Gaussian noise channel with a maximal or equal power constraint is at least (1/2) log n + O(1). This improves on the lower bound by Polyanskiy-Poor-Verdú (2010) and matches the upper bound proved by the same… (More)