Approximate fixed points of classical and quantum channels and robustness theory of quantum Markov chains

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• Robert Salzmann, DAMTP, University of Cambridge
• Wednesday 26 April 2023, 14:00-15:00
• MR11 (B1.39), CMS Pavilion B.

If you have a question about this talk, please contact Prof. Ramji Venkataramanan.

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The talk will focus on some preliminary results about approximate fixed points of channels. In particular it concerns the following question: Given a quantum (or classical) channel and a quantum state (or probability distribution) which is almost a fixed point of given channel, can we find a new channel and state close to the original ones such that those satisfy an exact fixed point equation? This question can be asked under many interesting constraints where the original channel and state are assumed to have certain structures which the new channel and state are supposed to satisfy as well. In this talk I will present an affirmative answer in the fully classical case. Moreover, as a motivating application of the abstract fixed point equation, I will talk about the robustness theory of so-called quantum Markov chains, which is a long standing open problem in quantum information theory

This talk is part of the Information Theory Seminar series.

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