Experimental investigation of dynamical invariants in bipartite entanglement

The nonconservation of entanglement, when two or more particles interact, sets it apart from other dynamical quantities, like energy and momentum, and does not allow the interpretation of the subtle dynamics of entanglement as a flow of this quantity between the constituents of the system. Nevertheless, we show that when the interaction between a qubit and its environment is described by an amplitude-decay channel, the conservation of the mean excitation number and the inclusion of a third party leads to an invariant expression involving the bipartite entanglement between each of the parties and the other two. We provide an experimental demonstration of this idea using entangled photons and generalize it to N-partite Greenberger-Horne-Zeilinger states.