New entangled state representation and its characteristics for the three compatible operators

Abstract

The eigenvector set of |φ(x, r₁, r₂)〉 with three compatible operators (

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\hat x_1 + \hat x_2 + \hat x_3$$\end{document}

,

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\hat p_2 + \hat p_3 - 2\hat p_1$$\end{document}

and

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\hat p_3 - \hat p_2$$\end{document}

) is constructed by virtue of Radon transformation of the Wigner operator and the technique of integration within an ordered product (IWOP) of operators. Its entanglement property is then revealed by deriving its standard Schmidt decomposition. |φ(x, r₁, r₂)〉 makes up a new quantum mechanical representation. A new three-mode squeezing operator is found by using this entangled state representation.

Keywords

Entangle State / Complete Relation / Radon Transformation / Quantum Mechanical Representation / Coherent Entangle State

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