Alexander Semjonowitsch Cholewo

Alexander Semjonowitsch Cholewo, Oberwolfach 2005

Alexander Semjonowitsch Cholewo ( Russian Александр Семёнович Холево , scientific transcription: Aleksandr Semënovič Cholevo, English transliteration: Alexander Semyonovich Kholevo or Holevo; born September 2, 1943 in Moscow ) is a Russian mathematician and mathematical scientist .

Life

Cholewo studied mathematics in Moscow, where he graduated in applied mathematics in 1966 and became a candidate (Russian doctorate ) in physics and mathematics in 1969 . He has been a mathematician at the Steklov Institute of the Russian Academy of Sciences since 1969 . In 1976 he completed his habilitation (Russian doctor). He was a professor at the Moscow Physics and Technology Institute and later gave lectures at Lomonosov University .

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Cholewo is mainly concerned with functional analysis and stochastic processes , especially with regard to quantum mechanics , and with quantum information theory (QIT), with fundamental work in the 1970s, long before QIT experienced a major boom in the 1990s. In 1973 he showed that surprisingly n qubits cannot represent more than n bits of classical information (Holevo's theorem). This is all the more surprising since it was later discovered (by Peter Shor and others) that quantum information systems provide a much more powerful predictability model than classical models. In addition, a much larger amount of information is required to define the quantum systems in which the information is encoded ( complex numbers, with n qubits, corresponding to the product state of n quantum mechanical two-state systems, except for a common complex factor). He also worked on the additivity problem of capacities (in the sense of Claude Shannon ) of communication channels and coding theorems in QIT. ${\ displaystyle 2 ^ {n} -1}$

He is also known for his fundamental work on the particular statistical problems that arise from quantum mechanics and on the mathematical foundations of quantum mechanics, as an extension of the Hilbert space formulation by John von Neumann from the 1930s. He summarized his research in his 1980 monograph. In the 1980s he investigated the development of the probability distributions of quantum mechanical systems from the underlying dynamics (time development) described by operators in Hilbert spaces (with semigroup structure).

He was invited speaker at the ICM in Madrid 2006 ( The additivity problem in quantum information theory ) and in Berkeley 1986 ( Conditionally positive functions in quantum probability ). In 1997 he received the Markov Prize of the Russian Academy of Sciences, in 1999 the Alexander von Humboldt Research Prize and in 1996 the International Quantum Communication Award . For 2015 he was awarded the Claude E. Shannon Award .

Fonts

Probabilistic and statistical aspects of Quantum Theory . North Holland 1982 (Russian Nauka 1980, 2nd edition 2003)
Quantum probability and quantum statistics . VINITI, Moscow 1991 (Russian)
An Introduction to Quantum Information Theory . Moscow 2002 (Russian)
Quantum coding theorems . In: Russian Mathematical Surveys . Vol. 53, 1998, pp. 1295-1331
Statistical structure of quantum theory . Lecture Notes in Physics, Springer Verlag, 2001
Quantum Systems, Channels, Information. A Mathematical Introduction , De Gruyter, 2012

literature

Osamu Hirota (Ed.): Quantum Information, Statistics, Probability. Dedicated to Alexander S. Holevo on the occasion of his 60th birthday. Rinton Press, Princeton NJ 2004, ISBN 1-58949-041-X .

Web links

Commons : Alexander Semjonowitsch Cholewo - collection of pictures, videos and audio files

Notes and references

↑ Cholewo: Some estimates of the information. transmitted over a quantum communication channel . In: Problems of Information Transmission . Volume 9, N3, 1973, pp. 3-11 (Russian). Suspected by JP Gordon at Bell Labs in 1964.
↑ In the foreword of his book Statistical Structure of Quantum Theory (2001), following Mark Kac's definition of probability theory as a measure theory “with a soul” (Measure Theory with a soul), he defined quantum mechanics as the theory of operators in Hilbert spaces with their statistical interpretation as a soul

personal data
SURNAME	Cholewo, Alexander Semjonowitsch
ALTERNATIVE NAMES	Холево, Александр Семёнович (Russian); Kholevo, Alexander Semyonovich (English transliteration); Holevo, Alexander Semyonovich (English transliteration); Cholevo, Aleksandr Semënovič (scientific transcription)
BRIEF DESCRIPTION	Russian mathematician and mathematical physicist
DATE OF BIRTH	September 2, 1943
PLACE OF BIRTH	Moscow

[1] Cholewo: Some estimates of the information. transmitted over a quantum communication channel . In: Problems of Information Transmission . Volume 9, N3, 1973, pp. 3-11 (Russian). Suspected by JP Gordon at Bell Labs in 1964.

[2] In the foreword of his book Statistical Structure of Quantum Theory (2001), following Mark Kac's definition of probability theory as a measure theory “with a soul” (Measure Theory with a soul), he defined quantum mechanics as the theory of operators in Hilbert spaces with their statistical interpretation as a soul