Von Neumann Entropy(VNE) $S(\rho)=S(\rho ')$ does not imply spectrum of $\rho$ equal to $\r

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We have mathematica code for three tuples \((p_1,p_2,p_3)\) showing that even we have VNE equal, we might have the tuples differ.
Plot3D[-Subscript[p, 1] Log[2, Subscript[p, 1]] - Subscript[p, 2] Log[2, Subscript[p, 2]] - (1 - Subscript[p, 1] - Subscript[p, 2]) Log[2, 1 - Subscript[p, 1] - Subscript[p, 2]], {Subscript[p, 1], 0, 1}, {Subscript[p, 2], 0, 1}, Mesh -> Automatic, MeshFunctions -> {#3 &}]

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