Name: Mathematical Challenges in Quantum Mechanics - Online Seminars
Start: 2023-11-08T09:00:00+01:00
End: 2024-05-31T23:00:00+02:00
Location: Online

Monday, November 6, 2023
Tuesday, November 7, 2023
Wednesday, November 8, 2023

11:30 AM MCQM PhD Lecture: Angela Capel Cuevas
MCQM PhD Lecture: Angela Capel Cuevas
11:30 AM - 12:30 PM
Title: Quantum entropy and trace inequalities Abstract: In this talk, I will give an elementary introduction to the subject of quantum entropies and trace inequalities, with a special focus on results that are relevant to quantum information theory. First, we will discuss various different notions of quantum entropies that extend those of classical entropies, and we will show several of their fundamental properties, in particular under the application of quantum channels. We will put a special focus on those properties that differ from their classical counterparts. Next, we will describe some contexts within quantum Shannon theory in which the use of quantum entropies is fundamental, such as for quantum hypothesis testing or to estimate quantum channel capacities.

2:15 PM MCQM Seminar: Nilanjana Datta
MCQM Seminar: Nilanjana Datta
2:15 PM - 3:15 PM
Title: Universal proofs of entropic continuity bounds via majorization flow Abstract: We employ majorization theory to obtain a powerful tool for deriving simple and universal proofs of continuity bounds for various entropies which are relevant in information theory. In obtaining this, we first state a more general result which may be of independent interest: a necessary and sufficient condition under which a state maximizes a concave, continuous, Gateaux-differentiable function in an epsilon-ball in trace distance. Examples of such a function include the von Neumann entropy, Renyi entropies, and the conditional entropy. In particular, by introducing a notion of majorization flow, we prove that the alpha-Rényi entropy is Lipschitz continuous, for alpha greater than 1, thus resolving an open problem and providing a substantial improvement over previously known bounds. This is joint work with Eric Hanson.
Thursday, November 9, 2023
Friday, November 10, 2023
Saturday, November 11, 2023
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Monday, November 13, 2023
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Monday, February 19, 2024
Tuesday, February 20, 2024
Wednesday, February 21, 2024

11:30 AM MCQM PhD Lecture: David Mitrouskas (ISTA Austria)
MCQM PhD Lecture: David Mitrouskas (ISTA Austria)
11:30 AM - 12:30 PM
TBA

2:15 PM MCQM Seminar: Fumio Hiroshima (Kyushu University)
MCQM Seminar: Fumio Hiroshima (Kyushu University)
2:15 PM - 3:15 PM
TBA
Thursday, February 22, 2024
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