  We study the effect of Kerr anharmonicity on the symmetry breaking phenomena
of coupled quantum oscillators. We study two types of symmetry-breaking
processes, namely the inhomogeneous steady state (or quantum oscillation death
state) and quantum chimera state. Remarkably, it is found that Kerr
nonlinearity hinders the process of symmetry-breaking in both the cases. We
establish our results using direct simulation of quantum master equation and
analysis of the stochastic semiclassical model. Interestingly, in the case of
quantum oscillation death, an increase in the strength of Kerr nonlinearity
tends to favor the symmetry and at the same time decreases the degree of
quantum mechanical entanglement. This study presents a useful mean to control
and engineer symmetry-breaking states for quantum technology.
