State Protection By Feed-forward Control In A Markovian Or A Non-markovian Environment

Any real quantum system will interact with its environment inevitably, which may cause decoherence. When we study the decoherence properties and dynamic behavior of quantum system, it is necessary to consider the characteristics of the surrounding environments. Different environments may have different effects on the dynamic behaviors of the system. Markovian process has been fully studied and people have made much study on the non-Markovian process. For the memoryless Markovian process, the coupling effect between system and the environment is relatively weak. In fact, the strong coupling effect between the system and environment also exists, so the non-Markovian process is also need to be considered. When we study the quantum system, we both consider the Markovian process and the non-Markovian process. In this paper we use the feed-forward control scheme to protect a one-qubit state and a two-qubit entangled state after passing a Markovian or a non-Markovian noise channel. The scheme is like this: Before the qubit enters the channel, the pre-weak measurement is made and according to different measurement results, a feed-forward is applied to make the quantum state not affected by noise channel, and the applying reversed operations and post-weak measurements make it restore to the protected state. This scheme only concerns about the noise channel not the protected state which is different from the other schemes. We show that one-qubit unknown state and two-qubit entangled state can be well protected by this scheme. For one-qubit state, the protecting effect is strongly dependent on the specific state, concretely for some states the effect is better for the non-Markovian noise channel, while for other states the effect is better for the Markovian one. For two-qubit entangled state, more entanglement can be created than not implementing any operations and for the non-Markovian environment the produced entanglement can preserve much longer than that in the Markovian environment.