  Decoherence effect on quantum entanglement of two optical qubits in a lossy
cavity interacting with a nonlinear medium (Kerr nonlinearity) is analyzed. The
qubits are assumed to be initially in the maximally entangled states (Bell or
Bell-like states) or the maximally entangled mixed states, on the example of
Werner and Werner-like states. Two kinds of measures of the entanglement are
considered: the concurrence to describe a decay of the entanglement of
formation of the qubits, and the negativity to determine a decay of the
entanglement cost under positive-partial-transpose-preserving operations. It is
observed that the Kerr nonlinearity, in the discussed decoherence model, does
not affect the entanglement of the qubits initially in the Bell or Werner
states, although the evolution of the qubits can depend on this nonlinearity
explicitly. However, it is shown that for the initial Bell-like state and the
corresponding Werner-like state, the loss of the entanglement can be
periodically reduced by inserting the Kerr nonlinearity in the lossy cavity.
Moreover, the relativity of the entanglement measures is demonstrated, to our
knowledge for the first time, as a result of a physical process.
