Karl Kraus (21 March 1938 – 9 June 1988) was a German

theoretical physicist Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimen ...

who made major contributions to the foundations of

quantum physics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...

Life and work

Kraus was born in 1938 in Hohenelbe/Giant Mountains, today

Vrchlabí Vrchlabí (; german: Hohenelbe, la, Albipolis) is a town in Trutnov District in the Hradec Králové Region of the Czech Republic. It has about 12,000 inhabitants. It lies at the foot of the Giant Mountains on the river Elbe. The town centre with ...

. After the war, he grew up in

Elsterwerda Elsterwerda (; Lower Sorbian: ''Wikow'') is a town in the Elbe-Elster district, in southwestern Brandenburg, Germany. It is situated on the Black Elster river, 48 km northwest of Dresden, and 11 km southeast of Bad Liebenwerda. Histo ...

and attended local schools. He studied physics from 1955 to 1960 at the

Humboldt University of Berlin Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...

(East) and the

Free University of Berlin The Free University of Berlin (, often abbreviated as FU Berlin or simply FU) is a public research university in Berlin, Germany. It is consistently ranked among Germany's best universities, with particular strengths in political science and t ...

(West). He graduated in 1962 with a thesis about

Lorentz Lorentz is a name derived from the Roman surname, Laurentius, which means "from Laurentum". It is the German form of Laurence. Notable people with the name include: Given name * Lorentz Aspen (born 1978), Norwegian heavy metal pianist and keyboar ...

's theory of gravity, carried out under the supervision of Kurt Just. Kraus then joined as an assistant to Günther Ludwig at the

University of Marburg The Philipps University of Marburg (german: Philipps-Universität Marburg) was founded in 1527 by Philip I, Landgrave of Hesse, which makes it one of Germany's oldest universities and the oldest still operating Protestant university in the wor ...

, where he qualified in 1966. In 1971, he accepted a professorship at the Institute of Physics of the

University of Würzburg The Julius Maximilian University of Würzburg (also referred to as the University of Würzburg, in German ''Julius-Maximilians-Universität Würzburg'') is a public research university in Würzburg, Germany. The University of Würzburg is one of ...

, where he established a

mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

working group on the topic of the foundations of quantum theory. In 1980 Kraus spent a sabbatical year at

UT Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 ...

with

John Archibald Wheeler John Archibald Wheeler (July 9, 1911April 13, 2008) was an American theoretical physicist. He was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in e ...

, Arno Böhm,

George Sudarshan Ennackal Chandy George Sudarshan (also known as E. C. G. Sudarshan; 16 September 1931 – 13 May 2018) was an Indian American theoretical physicist and a professor at the University of Texas. Sudarshan has been credited with numerous contrib ...

William Wootters William "Bill" Kent Wootters () is an American theoretical physicist, and one of the founders of the field of quantum information theory. In a 1982 joint paper with Wojciech H. Zurek, Wootters proved the no cloning theorem, at the same time as Den ...

, and

Wojciech Zurek Wojciech Hubert Zurek ( pl, Żurek; born 1951) is a theoretical physicist and a leading authority on quantum theory, especially decoherence and non-equilibrium dynamics of symmetry breaking and resulting defect generation (known as the Kibble–Zu ...

. Throughout his academic life, Kraus dealt with the question of the connection between the non-locality of the quantum world and the obvious locality of the classical world. He did work on this topic covering the Einstein–Podolsky–Rosen effect and issues regarding the

measurement problem In quantum mechanics, the measurement problem is the problem of how, or whether, wave function collapse occurs. The inability to observe such a collapse directly has given rise to different interpretations of quantum mechanics and poses a key se ...

in quantum theory, a problem which, in his opinion, was largely ignored in the

Copenhagen interpretation The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, principally attributed to Niels Bohr and Werner Heisenberg. It is one of the oldest of numerous proposed interpretations of quantum mechanics, as featu ...

by the founders of quantum theory. Some of Kraus' important publications on the measurement problem in quantum theory were: *Measuring processes in quantum mechanics I: Continuous observation and the watchdog effect. *Measuring processes in quantum mechanics II: The classical behavior of measuring instruments. *States, Effects, and Operations. In the book ''States, Effects, and Operations'' Kraus described the measurement process in quantum mechanics for the first time using the concept and mathematical formalism of a

quantum operation In quantum mechanics, a quantum operation (also known as quantum dynamical map or quantum process) is a mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. This was first discusse ...

, a special class of

maps A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes. Many maps are static, fixed to paper or some other durable medium, while others are dynamic or interactive. Although ...

density operator In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using ...

s. The representation he used for these maps is now known as the Kraus Representation,

Kraus Operator In quantum mechanics, a quantum operation (also known as quantum dynamical map or quantum process) is a mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. This was first discusse ...

Formalism or Operator-Sum Formalism, and is now frequently used in the field of

quantum information Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...

. The Kraus representation is based on a theorem of WF Stinespring about

completely positive In mathematics a positive map is a map between C*-algebras that sends positive elements to positive elements. A completely positive map is one which satisfies a stronger, more robust condition. Definition Let A and B be C*-algebras. A linea ...

images of finite-dimensional

C*-algebra In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra ''A'' of continuous ...

s. For a modern proof of the Kraus representation, which is based on a theorem of Man-Duen Choi instead of Stinespring's set, see M. Nielsen, I. Chuang. The issues discussed by Kraus regarding the foundations of quantum theory are still a current area of research. New theoretical advances are discussed in E. Joos, HD Zeh, C. Kiefer, D. Giulini, J. Kupsch, I.-O. Stamatescu. These decoherence theories have been combined with modern experiments, particularly those done by the groups of

Serge Haroche Serge Haroche (born 11 September 1944) is a French-Moroccan physicist who was awarded the 2012 Nobel Prize for Physics jointly with David J. Wineland for "ground-breaking experimental methods that enable measuring and manipulation of individual q ...

(Paris) and

Anton Zeilinger Anton Zeilinger (; born 20 May 1945) is an Austrian quantum physicist and Nobel laureate in physics of 2022. Zeilinger is professor of physics emeritus at the University of Vienna and senior scientist at the Institute for Quantum Optics and Qua ...

(Innsbruck, Vienna), in an attempt to use the measurement process in quantum theory to better understand relationship between quantum and classical world. In addition to mathematics and physics, Kraus had a special interest in biology, acquiring an extensive knowledge on the subject and even publishing some biological work. Karl Kraus died in 1988 at age 50 from the effects of cancer.

References

External links

Georg Reents: ''Nachruf auf Karl Kraus''

G. Reents, B. Schiekel: ''In memoriam Karl Kraus (1938–1988) – curriculum vitae''
(PDF; 67 kB) {{DEFAULTSORT:Kraus, Karl 1938 births 1988 deaths 20th-century German physicists Theoretical physicists People from Vrchlabí