Complementarity relations in multipath interferometers via decomposition of the uncertainty

Shuangshuang Fu, Xiaohui Li

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.

Gautam Sharma, Mohd Asad Siddiqui, Shiladitya Mal +2 more

Yue Sun, Ming‐Jing Zhao, Pengtong Li

The complementarity relations impose the constraints on different aspects of quantum states. We study the complementarity relation within a multi-path interferometer that includes detectors and quantum memory. Here we consider the mixed states as the input states. We establish a duality relation between the visibility and the path distinguishability. Based on this duality, two triality relations, one is related with visibility, path distinguishability, and mixedness, the other is related with visibility, path distinguishability, and entanglement, were derived respectively. Therefore, the role of entanglement in multi-path interferometer is characterized quantitatively. These complementarity relations are all complete for the two-path interferometer.

Yue Sun, Jingyan Liu, Peng-Tong Li +2 more

The complementarity relations in an interferometer reflect an important phenomenon in quantum mechanics: wave-particle duality. Here, we develop a method to quantify both wave and particle behaviors in a multi-path interferometer. In particular, we find that the trace distance is a good candidate for wave and particle measures. As a result, some duality relations and triality ralations are established respectively. This work not only extends the application of the trace distance to the interferometer, but also opens up new perspectives on the quantification of waveness and particleness.

Paul Busch, Christopher Shilladay

B. S. Thornton