  Investigating the quantum nature of gravity is an important issue in modern
physics. Recently, studies pertaining to the quantum superposition of
gravitational potential have garnered significant interest. Inspired by Mari
\textit{et al.} [Sci. Rep. {\bf 6} 22777 (2016)] and Baym and Ozawa [Proc.
Natl. Acad. Sci. U.S.A. {\bf 106}, 3035 (2009)], Belenchia \textit{et al.}
[Phys. Rev. D {\bf 98}, 126009 (2018)] considered a gedanken experiment
involving such a quantum superposition and mentioned that the superposition
renders causality and complementarity inconsistent. They resolved this
inconsistency by considering the quantized dynamical degrees of freedom of
gravity. This suggests a strong relationship between the quantum superposition
of the gravitational potential and the quantization of the gravitational field.
In our previous study [Phys. Rev. D {\bf 106}, 125002 (2022)], we have shown
that the quantum uncertainty of a field guarantees the consistency between
causality and complementarity. In this study, we focus on the entanglement
between two particles' states due to the electromagnetic/gravitational
potential and investigate its relationship with quantum uncertainty, causality,
and complementarity. Our numerical analyses show that the quantum uncertainty
of the electromagnetic/gravitational field results in vacuum fluctuations and
prohibits the entanglement between two particles' states when causality is
satisfied. We further demonstrate that complementarity holds when the particles
do not get entangled. The uncertainty relation does not cause the entanglement
between two particles' states, which guarantees complementarity.
