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arXiv:1907.05682 · Open Systems & Information Dynamics

The Legacy of George Sudarshan

Giuseppe Marmo, Saverio Pascazio

Published Sep 1, 2019• 1 citation
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Abstract

George Sudarshan was an eclectic thinker, and one of the most profound physicists of the last century. We review here a small part of his oeuvre, focusing on his pioneering contributions to the quantum Zeno effect, quantum channels (the Kraus–Sudarshan representation) and quantum semigroups (the Gorini–Kossakowski–Lindblad–Sudarshan equation). These topics are of crucial importance in the booming field of quantum mechanics and applications.

DOI
10.1142/s1230161219500112

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George Sudarshan was an eclectic thinker, and one of the most profound physicists of the last century. We review here a small part of his oeuvre, focusing on his pioneering contributions to the quantum Zeno effect, quantum channels (the Kraus–Sudarshan representation) and quantum semigroups (the Gorini–Kossakowski–Lindblad–Sudarshan equation). These topics are of crucial importance in the booming field of quantum mechanics and applications.
This note is written for the special issue of OSID dedicated to the 50th anniversary of the Gorini--Kossakowski--Lindblad--Sudarshan equation. Its purpose is not to give a comprehensive historical review, but rather to reconstruct, in a self-contained way, one logical route leading to the GKLS generator. The emphasis is placed on Kossakowski's structural insight: the combination of Markovianity, complete positivity, trace preservation, and the infinitesimal structure of quantum dynamical semigroups naturally leads to the celebrated form of the generator. I also include a few personal recollections of Andrzej Kossakowski, under whose guidance I spent one year as a postdoctoral researcher in 2003--2004.
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The theory of open quantum systems is one of the most essential tools for the development of quantum technologies. Furthermore, the Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) master equation plays a key role as it is the most general generator of Markovian dynamics in quantum systems. In this paper, we present this equation together with its derivation and methods of resolution. The presentation tries to be as self-contained and straightforward as possible to be useful to readers with no previous knowledge of this field.