Protecting quantum entanglement at finite temperature by the weak measurements

According to the map of a qubit, a scheme for protecting entanglement of two-qubit by the weak measurements at finite temperature is proposed. Since the choices of the channel parameters and initial states are very different for different weak measurement strengths, two local unitary equivalent initial entangled states vertical bar psi > and vertical bar phi > are chosen. Weak measurements are performed when two initial entangled states go through the generalized amplitude damping channel, and the analytical expressions of getting maximum concurrence entanglement C-r and weak measurement parameters m and n can be obtained by performing an overall optimization for four weak measurement parameters. What is more, the relationship between the weak measurement parameters and the channel parameters is further explored. Theoretical results show the entanglement protection project based on weak measurements can effectively enhance the entanglement and even prevent the sudden death of entanglement in some cases. When the channel parameter r is fixed, for different values of parameter p, the concurrence is centered at p = 0.5, and the weak measurement parameters of the maximum concurrence entanglement are the same as those for initial state vertical bar psi >, while they are different for initial state vertical bar phi >. Under the condition of different values of r, for the fixed p and initial state vertical bar psi > or vertical bar phi >, the weak measurement parameters remain constant as the entanglement reaches the maximum and the concurrence decreases with the increase of parameter r. Through the analysis of channel parameters, higher entanglement can be obtained by choosing appropriate channel parameters and initial state.