Protecting Quantum Enanglement By Weak Measurements In Finite Temperature

Quantum entanglement is the most core resource for quantum information. The tasks that classical information source cannot complete can be realized by the resource. Therefore, the primary task of quantum information is to obtain the high purity of entanglement. Such as quantum purification and photon pairs have been applied. Recently, a new quantum measurement--weak measurement is proposed to enhance the entanglement, which can amplify tiny signals and explain some surprising phenomenons that cannot be measured previous.Based on the definition and conditions of weak measurement, we first make specific inquiry for weak measurement, then applying it to protect entanglement. The article mainly includes the following two aspects:1. We study the changes of the output of the weak measurement on a qubit system when the pre- and postselection states are orthogonal or tend to orthogonal. When the states are orthogonal, we analyze the output theoretically, finding that the ability of amplifying tiny signals is limited. When the states tend to orthogonal,two cases are considered: first, preselections do not tend to the eigenstates of observations, the result is in accord with the result that the states tend to orthogonal. Second, preselections tend to the eigenstates, the result is affected by two different fidelity, which are defined as between preselections and eigenstates, between preselections and postselections, and the results have different limits under different conditions.2. We investigate how the entanglement evolves when two different initial Bell states go through the channel and whether improve entanglement by weak measurements and reversal measurements or not. At the same time, we will do an overall optimization for four weak measurement parameters in the generalized amplitude damping channel. The results find that weak measurements can improve entanglement,even can avoid entanglement sudden death in some cases; finding the way to obtain maximum entanglement and the relationship between weak measurement parameters and channel parameters. When the channel temperature parameter p is fixed, the concurrence decreases with the increase of parameters r for different initial states; when the channel parameter r is fixed, the concurrence is centered on p?5.0 and the intensity of weak measurement is different when the initial state is different. And through the analysis of the channel parameters, one can obtain higher entanglement by choosing the appropriate channel parameters and initial state.