  We investigate the Hermitian and the non-Hermitian dynamics of the mode
entanglement in two identical optical cavities coupled by a chiral mirror. By
employing the non-Hermitian quantum evolution, we calculate the logarithmic
negativity measure of entanglement for initially Fock, coherent and squeezed
states, separately. We verify the non-conservation of mean spin for the
initially coherent and squeezed states when the coupling is non-reciprocal and
report the associated spin noise for each case. We examine the effects of
non-conserved symmetries on the mode correlations and determine the degree of
non-reciprocal coupling to establish robust quantum entanglement.
