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- W2897216370 abstract "For multipartite states, we consider a notion of $D$ symmetry. For a system of $N$ qubits, it coincides with the usual permutational symmetry. In the case of $N$ qudits ($densuremath{ge}3$), the $D$ symmetry is stronger than the permutational one. For the space of all $mathrm{D}$-symmetric vectors in ${({mathbb{C}}^{d})}^{ensuremath{bigotimes}N}$, we define a basis composed of vectors ${|{R}_{N,d;k}ensuremath{rangle}:phantom{rule{0.16em}{0ex}}0ensuremath{le}kensuremath{le}N(densuremath{-}1)}$ which are analogs of Dicke states. The aim of this paper is to discuss the problem of separability of $D$-symmetric states which are diagonal in the basis ${|{R}_{N,d;k}ensuremath{rangle}}$. We show that if $N$ is even and $densuremath{ge}2$ is arbitrary then a positive partial transposition property is a necessary and sufficient condition of separability for $D$-invariant diagonal states. In this way, we generalize results obtained by Yu [Phys. Rev. A 94, 060101(R) (2016)] and Wolfe and Yelin [Phys. Rev. Lett. 112, 140402 (2014)]. Our strategy is to use some classical mathematical results on a moment problem." @default.
- W2897216370 created "2018-10-26" @default.
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- W2897216370 date "2019-02-08" @default.
- W2897216370 modified "2023-09-25" @default.
- W2897216370 title "Necessary and sufficient condition of separability for <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi mathvariant=normal>D</mml:mi></mml:math> -symmetric diagonal states" @default.
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- W2897216370 doi "https://doi.org/10.1103/physreva.99.022309" @default.
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