Effective entanglement recovery via operators

Entanglement is one of essential quantum resources in quantum information processing, playing an important role during quantum communication and computation. While any system unavoidably interacts with its surrounding environment, this thus will result in decoherence or dissipation effect. With this in mind, a natural question arises: how to recover quantum entanglement under decoherence inducing by the environmental noises. In this work, our attempt is to propose an effective strategy to optimally achieve entanglement recovery. Specifically, we derive a nontrivial condition satisfied by any operation U, i.e. (U⊗I)†(Ũ⊗I)=f(U)(I⊗I) , which will definitely recover the entanglement of an arbitrary two-qubit system, and more importantly offer an explicit physical explanation towards the intrinsic mechanics of the entanglement recovery. By means of derivations, we obtain the appropriate operational strength to realize optimal entanglement recovery through taking advantage of our proposed methods. As illustrations, we apply some local operations complying with our presented strategy on validly protecting entanglement, including PT -symmetry operation, quantum weak measurement and quantum reversal measurement.