What is it about?

In many situations, the evolution of a physical quantum system over time can naturally be described by a so-called Markov semigroup. Such an evolution in particular has the property that we can subdivide the evolution over a longer time interval into evolutions over arbitrarily small time intervals. We provide the first general necessary criteria for testing whether a given evolution can be subdivided in this way.

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Why is it important?

Understanding quantum (Non-)Markovianity has been an important challenge in quantum information theory since the GKLS characterization for generators of semigroups of quantum channels has been found. While there is still no single "correct" definition of quantum Markovianity, we provide the first general spectral criteria that can help decide whether a given quantum channel satisfies an important divisibilitly property related to quantum Markovianity.

Perspectives

This work goes back to my Bachelor's Thesis and therefore has been accompanying me for many years. I'm extremely happy that it turned into a project that I didn't work on alone, but together with a good friend and colleague.

Matthias C. Caro
Technische Universitat Munchen

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This page is a summary of: Necessary criteria for Markovian divisibility of linear maps, Journal of Mathematical Physics, April 2021, American Institute of Physics, DOI: 10.1063/5.0031760.
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