What is a Gaussian state? | Zendy

K. R. Parthasarathy | Zendy

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What is a Gaussian state?

Author(s) -

K. R. Parthasarathy

Publication year - 2010

Publication title -

communications on stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.224

H-Index - 10

eISSN - 2688-6669

pISSN - 0973-9599

DOI - 10.31390/cosa.4.2.02

Subject(s) - state (computer science) , gaussian , statistical physics , computer science , physics , algorithm , quantum mechanics

Stimulated by a remark of J. L. Doob at the beginning of Appen- dix I to Kai Lai Chung's English translation "Limit Distributions for Sums of Independent Variables" of the Russian classic by B. V. Gnedenko and A. N. Kolmogorov (5) we highlight the somewhat nonprobabilistic importance of characteristic functions and their positive definiteness property in a ped- agogical attempt to introduce the notion of a quantum Gaussian state and its properties to a classical probabilist. Such a presentation leads to some natural open problems on symmetry transformation properties of Gaussian states.

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