Rank-dependant factorization of entanglement evolution

• In some cases the complex entanglement evolution can be factorized on simple terms.
• We suggest factorization equations for multiqubit entanglement evolution.
• The factorization is solely defined by the rank of the final state density matrices.
• The factorization is independent on the local noisy channels and initial pure states.

The description of the entanglement evolution of a complex quantum system can be significantly simplified due to the symmetries of the initial state and the quantum channels, which simultaneously affect parts of the system. Using concurrence as the entanglement measure, we study the entanglement evolution of few qubit systems, when each of the qubits is affected by a local unital channel independently on the others. We found that for low-rank density matrices of the final quantum state, such complex entanglement dynamics can be completely described by a combination of independent factors representing the evolution of entanglement of the initial state, when just one of the qubits is affected by a local channel. We suggest necessary conditions for the rank of the density matrices to represent the entanglement evolution through the factors. Our finding is supported with analytical examples and numerical simulations.