Fig. 3
Nonclassicality of the qubit pair pure dephasing. a A schematic illustration of our extended spin-boson model, describing a pair of non-interacting qubits coupled to a common boson environment. b To simulate the qubit pair pure dephasing, \(\wp \left( {\boldsymbol{\lambda }} \right)\) is a (quasi-)distribution over \({\Bbb R}^3\) space spanned by λ3, λ8, and λ15. Here we show the six positive root vectors of \({\frak{s}}{\frak{u}}(4)\). Three simple root vectors (blue) define a new set of random variables. The other three non-simple root vectors (green) can be expressed as a combination of simple ones, e.g., α9 = α1 + α6 + α13. c The function \(\wp _{1,13}\left( {x_1,x_{13}} \right)\) distributes over the plane spanned by x1 and x13. For the case of Ohmic spectral density in the zero-temperature limit and ωc = 1, it shows manifest negative regions and therefore indicates the nonclassicality of the qubit pair pure dephasing
