Figure 3

Bounds for l ₁ coherence (a) and concurrence (b) of the two states in Eq. (24). In sub-figure (a), the black dotted line is the actual values of l ₁ coherence, the blue dashed line is upper bound on l ₁ coherence, the red solid line is lower bound on l ₁ coherence, and the green line represents the statistical average coherence of the superposed states, \({|\alpha |}^{2}{C}_{{l}_{1}}({\rm{\Phi }})+{|\beta |}^{2}{C}_{{l}_{1}}({\rm{\Psi }})\). In sub-figure (b), the black dotted line is the actual values of concurrence, the blue dashed line is upper bound on concurrence, the red solid line is lower bound on concurrence, and the green line represents the statistical average entanglement of the superposed states, \({|\alpha |}^{2}{E}_{C}({\rm{\Phi }})+{|\beta |}^{2}{E}_{C}({\rm{\Psi }})\). Note that coherence and entanglement are both non-negative.