On quantum Renyi entropies: a new definition and some properties

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 Amsterdam, The Netherlands Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore

[1]  M. Tomamichel A framework for non-asymptotic quantum information theory , 2012, 1203.2142.

[2]  Dong Yang,et al.  Strong converse for the classical capacity of entanglement-breaking channels , 2013, ArXiv.

[3]  S. Wehner,et al.  A strong converse for classical channel coding using entangled inputs. , 2009, Physical review letters.

[4]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5]  Patrick J. Coles,et al.  Uncertainty relations from simple entropic properties. , 2011, Physical review letters.

[6]  Tomohiro Ogawa,et al.  Strong converse and Stein's lemma in quantum hypothesis testing , 2000, IEEE Trans. Inf. Theory.

[7]  M. Sion On general minimax theorems , 1958 .

[8]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[9]  Marco Tomamichel,et al.  A Fully Quantum Asymptotic Equipartition Property , 2008, IEEE Transactions on Information Theory.

[10]  Renato Renner,et al.  Security of quantum key distribution , 2005, Ausgezeichnete Informatikdissertationen.

[11]  K. Audenaert,et al.  Quantum state discrimination bounds for finite sample size , 2012, 1204.0711.

[12]  Elliott H. Lieb,et al.  Monotonicity of a relative Rényi entropy , 2013, ArXiv.

[13]  Serge Fehr,et al.  On the Conditional Rényi Entropy , 2014, IEEE Transactions on Information Theory.

[14]  Maassen,et al.  Generalized entropic uncertainty relations. , 1988, Physical review letters.

[15]  D. Petz Quasi-entropies for finite quantum systems , 1986 .

[16]  Omar Fawzi,et al.  Entanglement Sampling and Applications , 2013, IEEE Transactions on Information Theory.

[17]  Nilanjana Datta,et al.  Min- and Max-Relative Entropies and a New Entanglement Monotone , 2008, IEEE Transactions on Information Theory.

[18]  Imre Csiszár Generalized cutoff rates and Renyi's information measures , 1995, IEEE Trans. Inf. Theory.

[19]  R. Renner,et al.  Uncertainty relation for smooth entropies. , 2010, Physical review letters.

[20]  O. Klein Zur quantenmechanischen Begründung des zweiten Hauptsatzes der Wärmelehre , 1931 .

[21]  Serge Fehr,et al.  On quantum R\'enyi entropies: a new definition, some properties and several conjectures , 2013 .