Optimal Quantum Parameter Estimation Of Spin Chain System Under Intrinsic Decoherence

Quantum entanglement as a basic resource for quantum information has been widely studied, it play an important role in the fields such as quantum computation, quantum teleportation, quantum communications. Very recently, studies found that entanglement can be used to improve the measurement precision of the estimation of parameters. However, any quantum system inevitably interacts with the surrounding environment, the ambient noise usually affects the physical performance of the system and leads quantum decoherence, which is the major obstacle to realize the quantum communication and quantum computers. So, how accurately measure or estimate the value of these parameters under the quantum decoherence system are the valuable subject we need to study.This paper will discuss the quantum inference theory under the decoherence system. Quantum Fisher information not only determines the lower bound of the variance of the unbiased estimator for parameter, but also can be used as a criterion of quantum entanglement. We use Milburn decoherence model to study the behavior of quantum decoherence evolution Fisher information on the Heisenberg spin chain with a magnetic field. Through Cramer-Rao inequality, the limit of parameters precision can be achieved under this intrinsic decoherence system. We found that under quantum decoherence systems, at the beginning, quantum Fisher information of parameters increase with time, it decays exponentially with time after a certain time. We also studied the relationship between quantum Fisher information and the entanglement(Negativity) of initial state.