Beyond I.I.D. in information theory
Monday 23rd July 2018 to Friday 27th July 2018
08:50 to 09:25  Registration  
09:25 to 09:35  Welcome from Christie Marr (INI Deputy Director)  
09:35 to 09:45  Welcome from the organisers  
09:45 to 10:30 
Renato Renner Entropy Accumulation: The Theorem and a Conjecture
The Entropy Accumulation Theorem is, roughly speaking,
the “BeyondIID”version of the Asymptotic Equipartition Property. It asserts
that the smooth minentropy of a system that consists of many parts is well
approximated by the sum of the von Neumann entropies of its subsystems
(evaluated for suitably chosen states of these subsystems). In my talk, I will
revisit this theorem and conjecture a generalisation. The latter would extend
the accumulation theorem to quantities other than entropies. 
INI 1  
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
Yiannis Kontoyiannis Lossy Compression Coding Theorems for Arbitrary Sources
We give a development of the theory of lossy data compression from the point of view of statistics. This is partly motivated by the enormous success of the statistical approach in lossless compression. A precise characterization of the fundamental limits of compression performance is given, for arbitrary data sources and with respect to general distortion measures. The emphasis is on nonasymptotic results and results that hold with high probability (and not just on the average). The starting point for this development is the observation that there is a precise correspondence between compression algorithms and probability distributions (in analogy with the Kraft inequality in lossless compression). This leads us to formulate a version of the celebrated Minimum Description Length (MDL) principle for lossy data compression. We discuss the consequences of the lossy MDL principle, and we explain how it can lead to practical design lessons for vector quantizer design. 
INI 1  
11:45 to 12:30 
Joe Renes On privacy amplification, lossy compression, and their duality to channel coding
We
examine the task of privacy amplification from informationtheoretic and
codingtheoretic points of view. In the former, we give a oneshot
characterization of the optimal rate of privacy amplification against classical
adversaries in terms of the optimal typeII error in asymmetric hypothesis
testing. This formulation can be easily computed to give finiteblocklength
bounds and turns out to be equivalent to smooth minentropy bounds by Renner
and Wolf [Asiacrypt 2005] and Watanabe and Hayashi [ISIT 2013], as well as a
bound in terms of the E divergence by Yang, Schaefer, and Poor
[arXiv:1706.03866 [cs.IT]]. In the latter, we show that protocols for privacy
amplification based on linear codes can be easily repurposed for channel
simulation. Combined with known relations between channel simulation and lossy
source coding, this implies that privacy amplification can be understood as a basic primitive for both
channel simulation and lossy compression. Applied to symmetric channels or
lossy compression settings, our construction leads to protocols of optimal rate
in the asymptotic i.i.d. limit. Finally, appealing to the notion of channel
duality recently detailed by us in [IEEE Trans. Info. Theory 64, 577 (2018)],
we show that linear errorcorrecting codes for symmetric channels with quantum
output can be transformed into linear lossy source coding schemes for classical
variables arising from the dual channel. This explains a “curious duality” in
these problems for the (selfdual) erasure channel observed by Martinian and
Yedidia [Allerton 2003; arXiv:cs/0408008] and partly anticipates recent results
on optimal lossy compression by polar and lowdensity generator matrix codes. 
INI 1  
12:30 to 14:00  Buffet Lunch at CMS  
14:00 to 14:45 
Guangyue Han InformationTheoretic Extensions of the ShannonNyquist Sampling Theorem
This talk will present informationtheoretic extensions of the classical ShannonNyquist sampling theorem and some of their applications. More specifically, we consider a continuoustime white Gaussian channel, which is typically formulated using a white Gaussian noise. A conventional way for examining such a channel is the sampling approach based on the ShannonNyquist sampling theorem, where the original continuoustime channel is converted to an equivalent discretetime channel, to which a great variety of established tools and methodology can be applied. However, one of the key issues of this scheme is that continuoustime feedback and memory cannot be incorporated into the channel model. It turns out that this issue can be circumvented by considering the Brownian motion formulation of a continuoustime white Gaussian channel. Nevertheless, as opposed to the white Gaussian noise formulation, a link that establishes the informationtheoretic connection between a continuous time channel under the Brownian motion formulation and its discretetime counterparts has long been missing. This paper is to fill this gap by establishing causalitypreserving connections between continuoustime Gaussian feedback/memory channels and their associated discretetime versions in the forms of sampling and approximation theorems, which we believe will help to contribute the further development of continuoustime information theory. Related Links 
INI 1  
14:45 to 15:30 
YoungHan Kim Shannon theory of ergodic sources and channels
Many
interesting source and channel models have memory. When the temporal dependence
fades away sufficiently fast (or more precisely, if the source or noise process
is ergodic), the standard coding techniques developed in classical Shannon
theory can be extended beyond i.i.d. memoryless cases, resulting in limiting
expressions for ratedistortion and capacity. The key idea behind this
extension is the ergodic decomposition of stationary processes, which was
utilized earlier by Gallager for ratedistortion theory of ergodic sources and
by Kim for capacity of ergodic channels with or without capacity. Such
interplay between information theory and ergodic theory is expected to play an
important role in problems other than pointtopoint source and channel coding.
Some technical background can be found in

INI 1  
15:30 to 16:00  Afternoon Tea  
16:00 to 16:45 
René Schwonnek Additivity of entropic uncertainty relations
We
consider the uncertainty between two pairs of local projective measurements
performed on a multipartite system. We show that the optimal bound in any
linear uncertainty relation, formulated in terms of the Shannon entropy, is
additive. This directly implies, against naive intuition, that the minimal
entropic uncertainty can always be realized by fully separable states. Hence,
in contradiction to proposals by other authors, no entanglement witness can be
constructed solely by comparing the attainable uncertainties of entangled and
separable states. However, our result gives rise to a huge simplification for
computing global uncertainty bounds as they now can be deduced from local ones.
Furthermore, we provide the natural generalization of the Maassen and Uffink
inequality for linear uncertainty relations with arbitrary positive
coefficients. 
INI 1  
16:45 to 17:30 
Zahra Baghali Khanian Compression of correlated quantumclassical sources, or: the price of ignorance
We
resume the investigation of the problem of
independent
local compression of correlated quantum sources,
the
classical case of which is covered by the celebrated
SlepianWolf
theorem.
We focus specifically on quantumclassical (qc)
sources,
for which one point of the rate region was
previously
determined by Devetak and Winter. Whereas the
Devetak
Winter point attains a ratesum equal to the von
Neumann
entropy of the joint source, here we show that the
full rate
region is much more complex due to the quantum
nature of
one of the sources. In particular, we determine the
full
rate region in the generic case, showing that all
other
points in the achievable region have a rate sum
strictly
larger than the joint entropy. We can interpret the
difference
as the price paid for the quantum encoder being
ignorant
of the classical side information. In the general
case, we
give an achievable rate region, via protocols that
are built
on the decoupling principle, state merging and
state
redistribution. It is matched almost by a
singleletter,
but still asymptotic, converse.

INI 1 
09:00 to 09:45 
Tobias Koch Rényi’s Information Dimension Beyond I.I.D.
Coauthor: Bernhard C. Geiger (Graz University of Technology) In 1959, Rényi proposed the information dimension and the ddimensional entropy to measure the information content of general random variables. Since then, it was shown that the information dimension is of relevance in various areas of information theory, including ratedistortion theory, almost lossless analog compression, or the analysis of interference channels. In this talk, I will propose a generalization of information dimension to stochastic processes, termed information dimension rate. I will then discuss some of its properties and compare it with other generalizations of information dimension available in the literature. I will further show that for Gaussian processes the information dimension rate permits a simple and intuitive characterization in terms of its spectral distribution function.Joint work with Bernhard Geiger (Graz University of Technology). Related Links

INI 1  
09:45 to 10:30 
Ramji Venkataramanan Strong converses and highdimensional statistical estimation problems
In many statistical inference problems, we wish to bound the
performance of any possible estimator. This can be seen as a converse result,
in a standard informationtheoretic sense. A standard approach in the
statistical literature is based on Fano’s inequality, which typically gives a
weak converse. We adapt these arguments by replacing Fano by more recent
informationtheoretic ideas, based on the work of Polyanskiy, Poor and Verdu.
This gives tighter lower bounds that can be easily computed and are
asymptotically sharp. We illustrate our technique in three applications:
density estimation, active learning of a binary classifier, and compressed
sensing, obtaining tighter risk lower bounds in each case. (joint with Oliver Johnson, see doi:10.1214/18EJS14) 
INI 1  
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
Philippe Faist Thermodynamic capacity of quantum processes
Thermodynamics imposes restrictions on what state transformations are possible. In the macroscopic limit of asymptotically many independent copies of a state—as for instance in the case of an ideal gas—the possible transformations become reversible and are fully characterized by the free energy. Here, we present a thermodynamic resource theory for quantum processes that also becomes reversible in the macroscopic limit. Namely, we identify a unique singleletter and additive quantity, the thermodynamic capacity, that characterizes the “thermodynamic value” of a quantum channel. As a consequence the work required to simulate many repetitions of a quantum process employing many repetitions of another quantum process becomes equal to the difference of the respective thermodynamic capacities. For our proof, we construct an explicit universal implementation of any quantum process using Gibbspreserving maps and a battery, requiring an amount of work asymptotically equal to the thermodynamic capacity. This implementation is also possible with thermal operations in the case of timecovariant quantum processes or when restricting to independent and identical inputs. In our derivations we make extensive use of SchurWeyl duality and informationtheoretic routines, leading to a generalized notion of quantum typical subspaces.
[joint work with Mario Berta and Fernando Brandão]

INI 1  
11:45 to 12:30 
Kun Fang Quantum Channel Simulation and the Channel's Smooth MaxInformation
Coauthors: Xin Wang (Centre for Quantum Software and Information, University of Technology Sydney), Marco Tomamichel (Centre for Quantum Software and Information, University of Technology Sydney), Mario Berta (Department of Computing, Imperial College London) We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the oneshot quantum simulation cost under nosignalling assisted codes are efficiently computable via semidefinite programming. Second, we introduce the channel's smooth maxinformation, which can be seen as a oneshot generalization of the mutual information of a quantum channel. We provide an exact operational interpretation of the channel's smooth maxinformation as the oneshot quantum simulation cost. Third, we derive the asymptotic equipartition property (AEP) of the channel's smooth maxinformation, i.e., it converges to the quantum mutual information of the channel in the independent and identically distributed asymptotic limit. This implies the quantum reverse Shannon theorem (QRST) in the presence of nosignalling correlations. Finally, we explore finite blocklength simulation cost of fundamental quantum channels and provide both numerical and analytical solutions. 
INI 1  
12:30 to 14:00  Buffet Lunch at CMS  
14:00 to 15:00  Open Problem Session  INI 1  
15:00 to 15:30  Afternoon Tea  
15:30 to 17:30  Poster Session  
17:30 to 18:30  Welcome Wine Reception at INI 
09:00 to 09:45 
Iman Marvian Coherence distillation machines are impossible in quantum thermodynamics
The role of coherence in quantum thermodynamics has been
extensively studied in the recent years and it is now wellunderstood that
coherence between different energy eigenstates is a resource independent of
other thermodynamics resources, such as work. A fundamental remaining open
question is whether the laws of quantum mechanics and thermodynamics allow the
existence a "coherence distillation machine", i.e. a machine that, by
possibly consuming work, obtains pure coherent states from mixed states, at a
nonzero rate. This question is related to another fundamental question:
Starting from many copies of noisy quantum clocks which are (approximately)
synchronized with a reference clock, can we distill synchronized clocks in pure
states, at a nonzero rate? In this paper we study quantities called
"coherence cost" and "distillable coherence", which
determine the rate of conversion of coherence in a standard pure state to
general mixed states, and vice versa, in the context of quantum thermodynamics.
We find that the coherence cost of any state (pure or mixed) is determined by
its Quantum Fisher Information (QFI), thereby revealing a novel operational
interpretation of this central quantity of quantum metrology. On the other
hand, we show that, surprisingly, distillable coherence is zero for typical
(fullrank) mixed states. Hence, we establish the impossibility of coherence
distillation machines in quantum thermodynamics, which can be compared with the
impossibility of perpetual motion machines or cloning machines. To establish
this result, we introduce a new additive quantifier of coherence, called the
"purity of coherence", and argue that its relation with QFI is
analogous to the relation between the free and total energies in
thermodynamics.

INI 1  
09:45 to 10:30 
Gerardo Adesso Gaussian quantum resource theories
Coauthors: Ludovico Lami (University of Nottingham), Bartosz Regula (University of Nottingham), Xin Wang (University of Technology Sydney), Rosanna Nichols (University of Nottingham), Andreas Winter (Universitat Autonoma de Barcelona) We develop a general framework characterizing the structure and properties of quantum resource theories for continuousvariable Gaussian states and Gaussian operations, establishing methods for their description and quantification. We show in particular that, under a few intuitive and physicallymotivated assumptions on the set of free states, no Gaussian quantum resource can be distilled with free Gaussian operations, even when an unlimited supply of the resource state is available. This places fundamental constraints on state transformations in all such Gaussian resource theories. We discuss in particular the applications to quantum entanglement, where we extend previously known results by showing that Gaussian entanglement cannot be distilled even with Gaussian operations preserving the positivity of the partial transpose, as well as to other Gaussian resources such as steering and optical nonclassicality. A unified semidefinite programming representation of all these reso urces is provided. Related Links

INI 1  
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
ZiWen Liu Resource theory of quantum channels 
INI 1  
11:45 to 12:30 
Mischa Woods The resource theoretic paradigm of Quantum Thermodynamics with Control
The
resource theory of quantum thermodynamics has been a very successful theory and
has
generated much follow up work
in the community. It requires energy preserving unitary operations
to be implemented over a
system, bath, and catalyst as part of its paradigm. So far, such unitary
operations have been
considered a “free” resource of the theory. However, this is only an
idealisation
of a necessarily inexact
process. Here, we include an additional auxiliary control system which can
autonomously implement the
unitary by turning “on/off” an interaction. However, the control
system will inevitable be
degraded by the backaction caused by the implementation of the unitary,
which cannot be perfectly
implemented. We derive limitations on the quality of the control devise so
that the laws of
thermodynamics do not change; and prove that the laws of quantum mechanics
allow
for a sufficiently small
backreaction so that the implementation of thermodynamic resource theoretic
operations can be achieved
without changing the paradigm, in addition to finding limitations for
others.

INI 1  
12:30 to 14:00  Buffet Lunch at CMS  
14:00 to 17:00  Free Afternoon 
09:00 to 09:45 
Pranab Sen Unions, intersections and a one shot quantum joint typicality lemma
A fundamental tool to prove inner bounds in classical
network information theory is the socalled `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 socalled `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 oneshot 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 oneshot 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 Some entropy properties of discrete random variables
It
is wellknown 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 logSobolev
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 logconcavity.

INI 1  
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
Mario Berta Partially smoothed information measures
Smooth entropies are a tool for quantifying resource
tradeoffs in (quantum) information theory and cryptography. In typical bi and
multipartite problems, however, some of the subsystems 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
subsystems fixed. This partial smoothing of information measures naturally
allows to give more refined characterizations of various informationtheoretic
problems in the oneshot setting. In particular, we immediately get asymptotic
secondorder characterizations for tasks such as privacy amplification against
classical side information or classical state splitting. For quantum problems
like state merging the general resource tradeoff is tightly characterized by
partially smoothed information measures as well. However, for quantum systems
we can so far only give the asymptotic firstorder expansion of these
quantities.

INI 1  
11:45 to 12:30 
Felix Leditzky 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 twoletter level, a substantial gap between the
threshold for zero quantum capacity and zero singleletter coherent
information, a big gap between singleletter 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 muchneeded
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 (19532018)  INI 1  
14:00 to 14:45 
Milan Mosonyi 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 Quantum fdivergences in von Neumann algebras
This talk is a comprehensive survey on recent developments of quantum divergences in general von Neumann algebras, including standard fdivergences, maximal fdivergences, and R\'enyi type divergences, whose mathematical backgrounds are Haagerup's L^pspaces and Araki's relative modular operator. Standard fdivergences were formerly studied by Petz in a bit more general form with name quasientropy, 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 fdivergence, from which most important properties of standard fdivergences follow immediately. We also go into standard R\'enyi divergences (as a variation of standard fdivergences) 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 BertaScholzTomamichel. Finally, we treat maximal fdivergences and discuss their definition, integral expression, and comparison with standard fdivergences. 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 Renyi relative entropies and noncommutative L_pspaces
The standard quantum Renyi relative entropies belong to the class of Petz quantum fdivergences 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 fdivergences 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 noncommutative L_pspaces 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 ArakiMasuda 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 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 maxmin 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) 
09:00 to 09:45 
Ivan Bardet Functional inequalities and the study of the speed of decoherence of an open quantum system 
INI 1  
09:45 to 10:30 
Sergii Strelchuk Classical and quantum features of Schur transform for information processing
It is wellknown 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 logSobolev 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
logconcavity.

INI 1  
10:30 to 11:00  Morning Coffee  
11:00 to 11:45 
Cambyse Rouzé Quantum reverse hypercontractivity: its tensorization and application to strong converses
Hypercontractivity and logSobolev inequalities have
found interesting applications in information theory in the past few years. In
particular, recently a strong converse bound for the hypothesis testing problem
have been proven based on the reverse hypercontractivity inequalities. This
talk is about the generalization of this application to the quantum setting.
First, the theory of quantum reverse hypercontractivity and its equivalence
with the logSobolev inequalities will be discussed. To this end, the problem
of the tensorization of quantum hypercontractivity inequalities will be
addressed. Next, it is shown how quantum reverse hypercontractivity
inequalities can be used for proving strong converse bounds in the quantum
setting. 
INI 1  
11:45 to 12:30 
Ángela Capel Quantum Conditional Relative Entropy and QuasiFactorization of the relative entropy
The existence of a positive logSobolev constant implies a
bound on the
mixing time of a quantum dissipative evolution under the
Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption
of a mixing condition in the Gibbs measure associated to their dynamics, via a
quasifactorization of the entropy in terms of the conditional entropy in some subalgebras. In this work we analyze analogous quasifactorization results in the quantum case. For that, we dene the quantum conditional relative entropy and prove several quasifactorization results for it. As an illustration of their potential, we use one of them to obtain a positive logSobolev constant for the heatbath dynamics with product fixed point. 
INI 1  
12:30 to 13:15 
Marius Junge Relative Entropy and Fisher Information
We show that in finite dimension the
set of generates satisfying a stable version of the logsobolev inequality for
the Fisher information is dense. The results is based on a new algebraic
property , valid for subordinates semigroups for sublabplacians on
compact Riemann manifolds which is then transferred to matrix algebras. Even in
the commutative setting the inequalities for subordinated sublaplacians are
entirely new. We also found counterexample for why a naive approach via
hypercontractivity is not expected to work in a matrixvalued setting,
similar to results by Bardet and collaborators.

INI 1  
13:15 to 15:15  Buffet Lunch at CMS 