Complementarity relations in multipath interferometers via decomposition of the uncertainty

In this paper, employing the metric-adjusted skew information, we bring up a family of decompositions of the total uncertainty as quantified by the variance into the quantum uncertainty and classical uncertainty. Based on the decompositions of uncertainty, we further establish a family of complete complementarity relations for predictability, interference, and correlation in multipath interferometers. Explicitly, we show that the predictability can be quantified by the (reverse) total uncertainty, the interference can be quantified by the quantum uncertainty, while the correlation can be quantified by the classical uncertainty. The family of complementarity relations established in this paper generalize previous characterizations of interference in multipath interferometers via the quantum Fisher information [Y. Sun et al., Phys. Rev. A 108, 062416 (2023)]. As an illustration, we calculate the relevant quantities for some extremal quantum states, and also give explicitly the complementarity relations in two-path interferometers, which demonstrate the validity of the quantifiers. We compare our results with two related complementarity relations established recently and highlight the main differences. The results obtained in this work reveal the close connections between uncertainty and complementarity.