Quantum Metrology And Decoherence

With the development of techniques in computer industries, the electronic chips tends to be extremely small. However, if chips ares smaller than a critical size, the traditional descriptions of the electronic circuits are invalid. Therefore, the theory of quantum infor-mation and computation appeared.In this thesis, I introduce quantum estimation and decoherence, including quantum Fisher information, spin squeezing, quantum phase transitions and hierarchy equation method. The Fisher information gives the ultra-limit of parameter estimation in experiments, and it is a entanglement detector. Decoherence is the main obstacle in the implement of quantum computing. The contents and results of the paper are listed below(1) In chapter 3, we employ the Lipkin-Meskho-Glick model to demonstrate the be-haviors of spin squeezing and quantum Fisher information in quantum phase transition. Compared with spin squeezing, quantum Fisher information is more suitable in character-izing the entanglement of the LMG model in difference phases. According to the inter-pretation of quantum Fisher information, the phase sensitivity of the ground state of the LMG model attains the Heisenberg limit in the symmetric broken phase, and only attains the standard quantum limit (shot-noise limit) in the symmetric phase.(2) In chapter 4,I discussed the master equation and hierarchy equation methods in regime of decoherence. We found that, if the bosonic bath is in zero temperature with a Lorentz type coupling spectrum, we can establish a set of hierarchy equations. With the hierarchy equations, we can avoid perturbative approximations.(3) In chapter 5,I discuss the decoherence of two qubits interacting with a common bath. Decoherence is the main obstacle in quantum computing. Traditional methods used in open dynamics usually involve many approximations, such as the Born approximation and Markov approximation. It is not surprising that entanglement can be generated for a separa-ble initial state, since the bath induces an effective qubit-qubit interaction. However, a key observation lies in the steady-state entanglement, which is determined only by the over-lap between the initial state and the decoherence-free state, independent of the system-bath coupling. This is because the dynamics of the qubit is restricted to a single-excitation sub-space. However, when the counter-rotating terms are accounted, double excitation occurs, and thus the steady-state entanglement vanishes for certain system-bath couplings.(4) In chapter 6,I discuss the quantum Fisher information of the Greenberg-Horne-Zeilinger (GHZ) state, which is a maximally entangled state, in the presence of deco-herece. I use three decoherence channels instead of specified physical models. The channels are amplitude-damping channel (ADC), phase-damping channel (PDC), and depolarizing channel (DPC). Although the channels seems to be toys as compared with concrete physical models, they indeed capture the essential physics of decoherence.We obtain analytical expressions for maximal mean QFI in terms of decoherence strength p. Based on these expressions, two remarkable results are found:(a) sudden changes of the maximal QFI are observed in all the three channels, and this sudden-change feature is similar to that in entanglement and spin squeezing, (b) For the ADC, after the sudden-changing point, the maximal mean QFI returns back to the shot-noise level with the increase of the decoherence strength. For the PDC, the maximal QFI decays to the shot-noise level and remains unchanged in this level with the increase of p. For the DPC, the QFI decays with the increase of p.The summary is given in chapter 7,...