Uncertainty relations in the product form<xref rid="cpb_27_7_070302fn1" ref-type="fn">*</xref><fn id="cpb_27_7_070302fn1"> <label>*</label><p>Project supported by the National Natural Science Foundation of China (Grant Nos. 11501153, 11461018, and 11531003) and the Simons Foundation (Grant No. 523868).</p></fn>

Uncertainty relations in the product form* *

Project supported by the National Natural Science Foundation of China (Grant Nos. 11501153, 11461018, and 11531003) and the Simons Foundation (Grant No. 523868).

Huang Xiaofen¹, Zhang Ting-Gui^{1, †}, Jing Naihuan^{2, 3}

(color online) The uncertainty relation for observables L_x and L_y at state |Ψ⟩: the blue curve is the lower bound in inequality (4) with the weight λ = 1/10, the red one is with the weight λ = 9/10, the black one stands for Mondal–Bagchi–Patis’ lower bound in inequality (14), and the green line denotes Schrödinger’ lower bound in inequality (3). As observed from the plot, the bound given by inequality (4) is one of the tightest bounds in the literature.