Fetching the paper…
Reading the bibliography…
The max-relative entropy together with its smoothed version is a basic tool in quantum information theory.
H. Umegaki, “Conditional expectation in an operator algebra,” Tohoku Mathematical Journal, Second Series
1954
Earlier work this paper cites.
John Wiley & Sons, 1968
R. Gallager, Information Theory and Reliable Communication · 1968
Earlier work this paper cites.
A. D. Wyner, “The wire-tap channel,” Bell system technical journal
1975
Earlier work this paper cites.
A. Uhlmann, “The ‘transition probability’ in the state space of a ∗ \ast -algebra,” Reports on Mathematical Physics
1976
Earlier work this paper cites.
J. L. Carter and M. N. Wegman, “Universal classes of hash functions,” Journal of Computer and System Sciences
1979
Earlier work this paper cites.
F. Hiai and D. Petz, “The proper formula for relative entropy and its asymptotics in quantum probability,” Communications in Mathematical Physics
1991
Earlier work this paper cites.
John Wiley & Sons, New York, 1991
T. M. Cover and J. A. Thomas, Elements of Information Theory · 1991
Earlier work this paper cites.
T. Han and S. Verdu, “Approximation theory of output statistics,” IEEE Transactions on Information Theory
1993
Earlier work this paper cites.
C. H. Bennett, G. Brassard, C. Crépeau, and U. M. Maurer, “Generalized privacy amplification,” IEEE Transactions on Information theory
1995
Earlier work this paper cites.
H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa, and B. Schumacher, “Noncommuting mixed states cannot be broadcast,” Physical Review Letters
1996
Earlier work this paper cites.
C. A. Fuchs and J. Van De Graaf, “Cryptographic distinguishability measures for quantum-mechanical states,” IEEE Transactions on Information Theory
1999
Earlier work this paper cites.
T. S. Han, “Hypothesis testing with the general source,” IEEE Transactions on Information Theory
2000
Earlier work this paper cites.
T. Ogawa and H. Nagaoka, “Strong converse and Stein’s lemma in quantum hypothesis testing,” IEEE Transactions on Information Theory
2000
Earlier work this paper cites.
M. Hayashi, “Optimal sequence of quantum measurements in the sense of Stein’s lemma in quantum hypothesis testing,” Journal of Physics A: Mathematical and General
2002
Earlier work this paper cites.
M. Hayashi and H. Nagaoka, “General formulas for capacity of classical-quantum channels,” IEEE Transactions on Information Theory
2003
Earlier work this paper cites.
Springer, 2003
T. S. Han, Information-Spectrum Methods in Information Theory · 2003
Earlier work this paper cites.
R. Renner, “Security of quantum key distribution,” Ph. D. Thesis
2005
Earlier work this paper cites.
I. Devetak and A. Winter, “Distillation of secret key and entanglement from quantum states,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
2005
Earlier work this paper cites.
A. Gilchrist, N. K. Langford, and M. A. Nielsen, “Distance measures to compare real and ideal quantum processes,” Physical Review A
2005
Earlier work this paper cites.
H. Nagaoka, “The converse part of the theorem for quantum Hoeffding bound,” arXiv preprint quant-ph/0611289
2006
Earlier work this paper cites.
H. Nagaoka and M. Hayashi, “An information-spectrum approach to classical and quantum hypothesis testing for simple hypotheses,” IEEE Transactions on Information Theory
2007
Cited alongside, same era.
K. M. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, “Discriminating states: The quantum chernoff bound,” Physical Review Letters
2007
Cited alongside, same era.
M. Hayashi, “Error exponent in asymmetric quantum hypothesis testing and its application to classical-quantum channel coding,” Physical Review A
2007
Cited alongside, same era.
K. M. Audenaert, M. Nussbaum, A. Szkoła, and F. Verstraete, “Asymptotic error rates in quantum hypothesis testing,” Communications in Mathematical Physics
2008
Cited alongside, same era.
N. Datta, “Min-and max-relative entropies and a new entanglement monotone,” IEEE Transactions on Information Theory
W. Matthews and S. Wehner, “Finite blocklength converse bounds for quantum channels,” IEEE Transactions on Information Theory
2014
Later among the works it cites.
K. Li, “Second-order asymptotics for quantum hypothesis testing,” The Annals of Statistics
2014
Later among the works it cites.
M. M. Wilde, A. Winter, and D. Yang, “Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Rényi relative entropy,” Communications in Mathematical Physics
2014
Later among the works it cites.
M. Tomamichel, M. Berta, and M. Hayashi, “Relating different quantum generalizations of the conditional Rényi entropy,” Journal of Mathematical Physics
2014
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2009
Cited alongside, same era.
M. Tomamichel, R. Colbeck, and R. Renner, “A fully quantum asymptotic equipartition property,” IEEE Transactions on Information Theory
2009
Cited alongside, same era.
M. Nussbaum and A. Szkoła, “The Chernoff lower bound for symmetric quantum hypothesis testing,” The Annals of Statistics
2009
Cited alongside, same era.
N. Datta and R. Renner, “Smooth entropies and the quantum information spectrum,” IEEE Transactions on Information Theory
2009
Cited alongside, same era.
M. Tomamichel, R. Colbeck, and R. Renner, “Duality between smooth min-and max-entropies,” IEEE Transactions on information theory
2010
Cited alongside, same era.
F. G. Brandao and M. B. Plenio, “A reversible theory of entanglement and its relation to the second law,” Communications in Mathematical Physics
2010
Cited alongside, same era.
M. Berta, M. Christandl, and R. Renner, “The quantum reverse Shannon theorem based on one-shot information theory,” Communications in Mathematical Physics
2011
Cited alongside, same era.
M. Tomamichel, C. Schaffner, A. Smith, and R. Renner, “Leftover hashing against quantum side information,” IEEE Transactions on Information Theory
2011
Cited alongside, same era.
2014
Later among the works it cites.
M. Hayashi, “Large deviation analysis for quantum security via smoothing of Rényi entropy of order 2,” IEEE Transactions on Information Theory
2014
Later among the works it cites.
Springer, 2015
M. Tomamichel, Quantum information processing with finite resources: mathematical foundations · 2015
Later among the works it cites.
M. Mosonyi and T. Ogawa, “Quantum hypothesis testing and the operational interpretation of the quantum Rényi relative entropies,” Communications in Mathematical Physics
2015
Later among the works it cites.
M. Hayashi, “Precise evaluation of leaked information with secure randomness extraction in the presence of quantum attacker,” Communications in Mathematical Physics
2015
Later among the works it cites.
M. Mosonyi and T. Ogawa, “Two approaches to obtain the strong converse exponent of quantum hypothesis testing for general sequences of quantum states,” IEEE Transactions on Information Theory
2015
Later among the works it cites.
M. Hayashi, “Security analysis of ε \varepsilon -almost dual universal2 hash functions: smoothing of min entropy versus smoothing of Rényi entropy of order 2,” IEEE Transactions on Information Theory
2016
Later among the works it cites.
M. Hayashi and V. Y. Tan, “Equivocations, exponents, and second-order coding rates under various Rényi information measures,” IEEE Transactions on Information Theory
2016
Later among the works it cites.
T. Cooney, M. Mosonyi, and M. M. Wilde, “Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication,” Communications in Mathematical Physics
2016
Later among the works it cites.
M. Hayashi and M. Tomamichel, “Correlation detection and an operational interpretation of the Rényi mutual information,” Journal of Mathematical Physics
2016
Later among the works it cites.
F. Leditzky, M. M. Wilde, and N. Datta, “Strong converse theorems using Rényi entropies,” Journal of Mathematical Physics
2016
Later among the works it cites.
M. Mosonyi and T. Ogawa, “Strong converse exponent for classical-quantum channel coding,” Communications in Mathematical Physics
2017
Later among the works it cites.
H.-C. Cheng, E. P. Hanson, N. Datta, and M.-H. Hsieh, “Non-asymptotic classical data compression with quantum side information,” IEEE Transactions on Information Theory
2020
Later among the works it cites.
A. Anshu, M. Berta, R. Jain, and M. Tomamichel, “Partially smoothed information measures,” IEEE Transactions on Information Theory
2020
Later among the works it cites.