Göran Lindblad

Göran Lindblad passed away near his home in Johanneshov in Stockholm, Sweden, at the age of 82.

Lindblad spent all of his career in Sweden, at KTH–Royal Institute of Technology. His area of research was mathematical physics, the area of physics where the objective is to mathematically prove results of physical importance. Notwithstanding the increased difficulty posed by the requirement of rigor, Lindblad made physical discoveries of the highest importance that have had manifold practical applications and uses.

In the 1970s Lindblad developed the systematic theory of open quantum systems, which are not isolated but interact with an environment. He showed that if such systems have the Markov property of evolving in time without remembering their previous state, then this evolution has to be of a form today generally called the Lindblad equation . Analogous results were obtained for finite-dimensional Hilbert spaces at about the same time by Gorini, Kossakowski, and Sudarshan , and the form of the evolution operator appeared earlier in the work of Davies and Kossakowski (see here , for example). Nevertheless, it is Lindblad who is generally credited in the first place. Lindblad’s formulation focused more generally on the infinite-dimensional case, thus highlighting the norm continuity assumption and boundedness of the generator. He also derived the most general completely positive Markovian semigroup master equation for the dynamics of the density matrix.

The Lindblad equation is completely fundamental in modern quantum technology and is used in the theory and even more practically in applications ranging from laser physics, quantum optics, and quantum chemistry to estimates of errors in quantum computations and theoretical limits on what can be done with quantum computers. Lindblad therefore belongs to the very restricted group of physicists who could have answered back to Dirac when he reportedly remarked to Feynman, “I have an equation. What is your equation?”

During the same time in the 1970s, Lindblad was also one of the first who worked on information, entropy, and distinguishability as a quantum-mechanical concept, and the first who showed that such distinguishability cannot increase when sent through a general quantum channel. For instance, this means that quantum mechanical distinguishability encoded into photons in any entangled states whatsoever and then sent through a glass fiber cable can only decrease.

Quantum communication has today become the science and technology that aims to describe and quantify quantum information and how it is transferred from one medium to another or from one point to another. Transmission of a few qubits over the whole Earth has been demonstrated experimentally via satellite and exists as several functional commercial Earth-bound services for distances from tens to hundreds of kilometers. Lindblad was one of a small group of visionaries who laid the foundations so that this today has become a reality.

In his work Lindblad was a lone ranger. Most of his scientific articles have but one single author. He was a polite and friendly, but also taciturn, man. He was an at least partly feared lecturer. He treated students as if they were his equals in knowledge and understanding, and he sometimes faced difficulties reaching everyone. In his teaching he mainly used his own lecture notes, which for those in the know were often superior to textbooks in clarity and stringency but to some others incomprehensibly compact.

In his prime, Lindblad’s arguments and ways of stating his results were not seldom too mathematical to be fully appreciated by physicists in his country. His motivations, on the other hand, often built on deep physical intuition, making them inaccessible to mathematicians. During his active career, Lindblad accordingly did not receive any major signs of distinction from the Swedish scientific community. After his retirement, and with the explosion of interest in quantum science and technology, Lindblad’s increasing international fame was finally fully reflected in appreciation at home.

A great man, a man who accomplished great things, has left the world of science.

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