Schedule for the QMATH Masterclass 2022
Additional information for everyone already in Copenhagen on Sunday evening (21.08.2022). We will be meeting at Blågårds Plads for an informal welcome drink before the school with everyone who is interested - just look around in the vicinity of Blågård's Pharmacy from around 20:00.
Diner location: Restaurant FOOD CLUB, Sortedam Dossering 7C, 2200 København N
Schedule QMATH Masterclass 2022 | |||||
Location: |
HCØ Building, Universitetsparken 5, 2100 København |
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Mo | Di | Mi | Do | Fr | |
lecture hall | Aud 4 | Aud 4 | Aud 4 | Aud 4 | Aud 1 |
9:00-10:40 | Registration | Graeme Smith | Raymond Yeung | Christoph Hirche | Marco Tomamichel |
10:40-11:00 | Welcome | Coffee break | Coffee break | Coffee break | Coffee break |
11:00-12:40 | Graeme Smith | Omar Fawzi | Matthias Christandl | Marco Tomamichel | Andreas Winter |
12:40-14:00 | Lunch | Lunch | 12:40-13:15 Lunch | Lunch | Open Problem Lunch |
14:00-15:40 | Omar Fawzi | Matthias Christandl | 13:15-14:10 Paula Belzig | Christoph Hirche | |
15:40-16:00 | Coffee break | Coffee break | Canoeing/Free afternoon | Coffee break | |
16:00-17:00 | Jan Philip Solovej | Poster & Pizza | 15.30-17.00 Andreas Winter | ||
17.30 Welcome Receiption | 18.45 Masterclass dinner | ||||
Meeting time Canoeing:15:45 Meeting point: Nybro Boat & Canoe Rental, Nybrovej 384, 2800 Kongens Lyngby |
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Invited Speaker:
Matthias Christandl:
Title: Quantum functionals
Abstract: Von Neumann entropy (as an extension of Shannon's) appears in information theory through the asymptotic equipartition theorem: by allowing small probabilities of error and going to large block lengths, we can remarkably compress information to its value. Is there also an operational home for John's entropy in the zero-error world? I will report on our findings from the strange worlds of tensors, algebraic complexity and SLOCC (oh my). In the first lecture I will define the quantum functionals. In the second, I will discuss properties, extensions and - most importantly - the open questions. Oh, and inequalities. I might also attempt some live quantum demonstration.
Optional reading preparation
https://arxiv.org/abs/1208.0365
https://arxiv.org/abs/1709.07851
There are also some related talks online on the general topic, e.g. https://youtu.be/sI3srxec-Vk
Omar Fawzi:
Title: Chain rules for quantum (relative) entropies
Abstract: Chain rules provide an important tool in information theory to reduce the (relative) entropy of a multipartite system to a sum of (relative) entropies of individual systems. Even though many such chain rules are straightforward to prove for classical systems, the quantum case is significantly more complicated due to the difficulty of defining conditional states. This is particularly the case when dealing with relative or R\'enyi entropies.
In these lectures, I plan to focus on the chain rules for the conditional and relative R\'enyi entropies that were developed to establish entropy accumulation theorems. Entropy accumulation theorems can be seen as generalizations of the asymptotic equipartition property for systems that are not independent and identically distributed.
Some references for the lectures: https://arxiv.org/abs/1607.01796, https://arxiv.org/abs/1909.05826, https://arxiv.org/abs/2007.12576, https://arxiv.org/abs/2203.04989, https://arxiv.org/abs/2204.11153
Christoph Hirche:
Title: Contraction coefficients, partial orders and applications
Graeme Smith:
Title: Additivity and Nonadditivity in quantum information theory
Abstract: I will discuss a selection of questions about the additivity and nonadditivity of entropic formulas that arise in quantum shannon theory.
Marco Tomamichel:
Title: Quantum Rényi divergence – an attempt at an axiomatic approach
Abstract: I’ll show how classical Rényi divergences can be derived from information-theoretic axioms quite satisfactorily and attempt to do the same thing for quantum Rényi divergences. The attempt will fail miserably, but the open questions it reveals should nonetheless be interesting.
Andreas Winter:
Title: Entropy inequalities: beyond strong subadditivity?
Abstract: What are the constraints that the von Neumann entropies
of the 2^n possible marginals of an n-party quantum state have
to obey? Similarly for the Shannon entropy of n random variables?
Pippenger called these “the laws of (quantum) information theory”,
among them subadditivity and strong subadditivity, and while we
know a few of them, we seem to me missing many. In fact, it is
known that both classically and quantumly, the set of entropy
vectors is essentially a convex cone, so the laws in question
naturally take the form of homogeneous convex inequalities. More
specifically, we can describe the classical and entropy cones
for n parties by linear information inequalities. Starting with
Zhang and Yeung, Dougherty et al. and finally Matus have shown
that 4-partite Shannon entropies satisfy infinitely many inequalities
beyond the standard ones, the “Shannon inequalities", which
define a polyhedral cone. Matus’s result implies that the entropy
cone of 4 random variables is not polyhedral.
I will review progress towards finding non-von-Neumann inequalities
in the quantum case, commenting on the case of Rényi entropies as well.
Raymond Yeung:
Title: Entropy Inequalities and Machine Proving
Local Speakers:
Paula Belzig:
Title: Fault-tolerant entanglement-assisted communication
Abstract: The process of communicating information between two devices, a sender and a receiver, is modelled by a noisy channel which maps an encoded message to a potentially corrupted output signal. Then, the capacity of a given channel quantifies the optimal asymptotic rate of sending information over the channel where the original message can always be recovered. Usually, the study of capacities assumes that the circuits which the sender and the receiver use for encoding and decoding the information consist of perfect gates without noise. However, this is not believed to be true for quantum devices manufactured in the near-term and even long-term future. Assuming that each gate is affected by an error with probability, we use techniques from fault-tolerant quantum computing to prove coding theorems for a fault-tolerant version of entanglement-assisted classical capacity, devising a coding technique for a fault-tolerant version of this type of capacity and proving in particular that it approaches the usual, faultless case for vanishing gate error probability.
Jan Philip Solovej
Title: Minimal Output Entropy for Invariant Quantum Channels
Abstract: I will introduce quantum channels, i.e., completely positive
trace preserving maps, that are invariant under group actions. For the
groups SU(N) and SU(1,1) I will introduce explicit invariant quantum
channels. For certain representations of SU(N) I will determine the
minimal output entropy of these, while for SU(1,1) there are essentially
only conjectures. I will briefly mention the relation to the Wehrl classical entropy
of quantum states and discuss what is known for the minimal Wehrl entropy.
This is joint work with Elliott Lieb.