09:00 to 09:45 Pranab Sen (Tata Institute of Fundamental Research)Unions, intersections and a one shot quantum joint typicality lemma A fundamental tool to prove inner bounds in classical network information theory is the so-called conditional joint typicality lemma'. In addition to the lemma, one often uses unions and intersections of typical sets in the inner bound arguments without so much as giving them a second thought. These arguments fail spectacularly in the quantum setting. This bottleneck shows up in the fact that so-called simultaneous decoders', as opposed to `successive cancellation decoders', are known for very few channels in quantum network information theory. In this talk we shall see how to overcome the bottleneck by proving for the first time a one-shot quantum joint typicality lemma with robust union and intersection properties. To do so we develop two novel tools  in quantum information theory, which we call tilting and smoothing, which should be of independent interest. Our joint typicality lemma allows us to construct simultaneous quantum decoders for many multiterminal quantum channels and gives a  powerful tool to extend many results in classical network information theory to the one-shot quantum setting. We shall see a glimpse of this in the talk by constructing a one shot simultaneous decoder for the quantum multiple access channel with an arbitrary number of senders. Our one shot rates reduce to the known optimal rates when restricted to the asymptotic iid setting, which were previously obtained by successive cancellation and time sharing. INI 1 09:45 to 10:30 Oliver Johnson (University of Bristol)Some entropy properties of discrete random variables It is well-known that Gaussian random variables have many attractive properties: they are maximum entropy, they are stable under addition and scaling, they give equality in the Entropy Power Inequality (and hence give sharp log-Sobolev inequalities) and have good entropy concavity properties. I will discuss the extent to which results of this kind can be formulated for discrete random variables, and how they relate to ideas of discrete log-concavity. INI 1 10:30 to 11:00 Morning Coffee 11:00 to 11:45 Mario Berta (Imperial College London)Partially smoothed information measures Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected by the standard smoothing of information measures over a ball of close states. We propose to smooth instead only over a ball of close states which also have some of the reduced states on the relevant sub-systems fixed. This partial smoothing of information measures naturally allows to give more refined characterizations of various information-theoretic problems in the one-shot setting. In particular, we immediately get asymptotic second-order characterizations for tasks such as privacy amplification against classical side information or classical state splitting. For quantum problems like state merging the general resource trade-off is tightly characterized by partially smoothed information measures as well. However, for quantum systems we can so far only give the asymptotic first-order expansion of these quantities. INI 1 11:45 to 12:30 Felix Leditzky (University of Colorado)Dephrasure channel and superadditivity of coherent information The quantum capacity of a quantum channel captures its capability for noiseless quantum communication. It lies at the heart of quantum information theory. Unfortunately, our poor understanding of nonadditivity of coherent information makes it hard to understand the quantum capacity of all but very special channels. In this paper, we consider the dephrasure channel, which is the concatenation of a dephasing channel and an erasure channel. This very simple channel displays remarkably rich and exotic properties: we find nonadditivity of coherent information at the two-letter level, a substantial gap between the threshold for zero quantum capacity and zero single-letter coherent information, a big gap between single-letter coherent and private informations. Its clean form simplifies the evaluation of coherent information substantially and, as such, we hope that the dephrasure channel will provide a much-needed laboratory for the testing of new ideas about nonadditivity. INI 1 12:30 to 14:00 Buffet Lunch at CMS 13:55 to 17:30 Afternoon Session: In memory of Dénes Petz (1953-2018) INI 1 14:00 to 14:45 Milan Mosonyi (Budapest University of Technology and Economics)Dénes Petz' legacy in quantum information theory In this talk we give an overview of a subjective selection of Dénes Petz's many results on quantum entropies and their impact on quantum information theory, with a special emphasis on recent results inspired by them. INI 1 14:45 to 15:30 Fumio Hiai (Tohoku University)Quantum f-divergences in von Neumann algebras This talk is a comprehensive survey on recent developments of quantum divergences in general von Neumann algebras, including standard f-divergences, maximal f-divergences, and R\'enyi type divergences, whose mathematical backgrounds are Haagerup's L^p-spaces and Araki's relative modular operator. Standard f-divergences were formerly studied by Petz in a bit more general form with name quasi-entropy, whose most familiar one is the relative entropy initiated by Umegaki and extended to general von Neumann algebras by Araki. We extend Kosaki's variational expression of the relative entropy to an arbitrary standard f-divergence, from which most important properties of standard f-divergences follow immediately. We also go into standard R\'enyi divergences (as a variation of standard f-divergences) in some detail, and touch briefly sandwiched R\'enyi divergences in von Neumann algebras, which have recently been developed by Jen\v cov\'a and Berta-Scholz-Tomamichel. Finally, we treat maximal f-divergences and discuss their definition, integral expression, and comparison with standard f-divergences. This talk is dedicated to the memory of D\'enes Petz. INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 16:45 Anna Jenčová (Slovak Academy of Sciences)Renyi relative entropies and noncommutative L_p-spaces The standard quantum Renyi relative entropies belong to the class of Petz quantum f-divergences and have a number of applications in quantum information theory, including and operational interpretation as error exponents in quantum hypothesis testing. In the last couple of years, the sandwiched version of Renyi relative entropies gained attention for their applications in various strong converse results. While the Petz f-divergences are defined for arbitrary von Neumann algebras, the sandwiched version was introduced for density matrices. In this contribution, it is shown that these quantities can be extended to infinite dimensions. To this end, we use the interpolating family of non-commutative L_p-spaces with respect to a state, defined by Kosaki. This definition provides us with tools for proving a number of properties of the sandwiched Renyi entropies, in particular the data processing inequality with respect to normal unital (completely) positive maps. It is also shown that this definition coincides with the previously introduced Araki-Masuda divergences by Berta et. al.The notion of sufficient (or reversible) quantum channels was introduced and studied by Petz. One of the fundamental results in this context is the fact that equality in the data processing inequality for the quantum relative entropy is equivalent to sufficiency of the channel. We extend this result for sandwiched Renyi relative entropies. See arXiv:1609.08462 and arXiv:1707.00047 for more details. INI 1 16:45 to 17:30 Beth Ruskai (University of Massachusetts Lowell)Using local additivity to find examples of superadditivity of quantum channels The local additivity of minimal output entropy can be extended to local additivity of maximal relative entropy with respect to a fixed reference state. This can be exploited to test channels for superadditivity of Holevo capacity with numerical effort comparable to searching for the minimal output entropy. Local maxima which do not arise from product inputs play a key role.  Moreover, evidence of superadditivity can be found even if the additivity violation itself is too small to be seen numerically.  A  max-min expression for the capacity, dues to Petz, et al, plays a key role. INI 1 19:00 to 22:00 Formal Dinner at Pembroke College (Old Library)