A Brief History of the GKLS Equation

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Abstract

We reconstruct the chain of events, intuitions and ideas that led to the formulation of the Gorini, Kossakowski, Lindblad and Sudarshan equation.

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Quantum entanglement

Ryszard Horodecki, Karol Horodecki, Pawel Horodecki … (2007)

All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.

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Completely positive maps and entropy inequalities

Göran Lindblad (1975)

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Model for Nuclear Reactions with Neutrons

C. E. Porter, V. F. Weisskopf, H. Feshbach (1954)

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Publication date Created: 16 October 2017

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ArXiV ID: 1710.05993

SO-VID: 3dbc8744-41b6-4d1a-8792-ded6cbf72533

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http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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Comments Based on a talk given by D.C. at the 48th Symposium on Mathematical Physics "Gorini-Kossakowski-Lindblad-Sudarshan Master Equation - 40 Years After" (Toru\'n, June 10-12, 2016). To be published in the special volume of OSID

Categories quant-ph physics.hist-ph

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A Brief History of the GKLS Equation

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Peter Lang Books - History

Most cited references 20

Quantum entanglement

Completely positive maps and entropy inequalities

Model for Nuclear Reactions with Neutrons

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History

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