Rank-dependant factorization of entanglement evolution

Abstract

Symmetries of the initial state of a quantum system and the quantum channels, which simultaneously affect parts of the system, can significantly simplify the description of the entanglement evolution. 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 channel independently of the others. We show 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.