On definition of quantum tomography via the Sobolev embedding theorem
G.G. Amosov, Ya.A. Korennoy
TL;DR
This paper establishes conditions for defining quantum tomography tools like Wigner functions and optical tomograms using Sobolev embedding, enhancing the mathematical foundation of quantum state analysis.
Contribution
It introduces a Sobolev embedding-based framework to ensure proper definition of quantum tomography functions and links various quantum representations.
Findings
Provided sufficient conditions for quantum state kernels
Ensured correct definition of Wigner functions and tomograms
Discussed the fractional Fourier transform within this framework
Abstract
We obtain sufficient conditions on kernels of quantum states under which Wigner functions, optical quantum tomograms and linking their formulas are correctly defined. Our approach is based upon the Sobolev embedding theorem. The transition probability formula and the fractional Fourier transform are discussed in this framework.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics · Mathematical functions and polynomials