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[The density matrix of a Werner quantum state is invariant under all unitary operators of the form U⊗U\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U\otimes U$$\end{document}. That is, its ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document} matrix satisfies ρ=(U⊗U)ρ(U†⊗U†)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho =(U\otimes U)\rho (U^{\dagger }\otimes U^{\dagger })$$\end{document} for all unitary operators U acting on the Hilbert space [1]. Werner-like states as implemented in quantum games in this chapter are linear combinations of a maximally entangled and an uncorrelated mixed state that will act as alternative initial states in the EWL model.]
Published: May 22, 2019
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