Error-corrected quantum metrology

Quantum metrology, which studies parameter estimation in quantum systems, has many applications in science and technology ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on the estimation precision, called the Heisenberg limit (HL), which bears a quadratic enhancement over the standard quantum limit (SQL) determined by classical statistics. The HL is achievable in ideal quantum devices, but is not always achievable in presence of noise. Quantum error correction (QEC), as a standard tool in quantum information science to combat the effect of noise, was considered as a candidate to enhance quantum metrology in noisy environment. This thesis studies metrological limits in noisy quantum systems and proposes QEC protocols to achieve these limits. First, we consider Hamiltonian estimation under Markovian noise and obtain a necessary and sufficient condition called the ``Hamiltonian-not-in-Lindblad-span\u27\u27 condition to achieve the HL. When it holds, we provide ancilla-assisted QEC protocols achieving the HL; when it fails, the SQL is inevitable even using arbitrary quantum controls, but approximate QEC protocols can achieve the optimal SQL coefficient. We generalize the results to parameter estimation in quantum channels, where we obtain the ``Hamiltonian-not-in-Kraus-span\u27\u27 condition and find explicit formulas for asymptotic estimation precision by showing attainability of previously established bounds using QEC protocols. All QEC protocols are optimized via semidefinite programming. Finally, we show that reversely, metrological bounds also restrict the performance of error-correcting codes by deriving a powerful bound in covariant QEC

Achieving the Heisenberg limit in quantum metrology using quantum error correction

Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed which suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.Comment: 16 pages, 2 figures, see also arXiv:1704.0628

Marginal abatement costs of carbon dioxide in China: A nonparametric analysis

AbstractThe estimates of abatement costs about CO2 can provide useful information for policy-makers. With the framework of production theory, a marginal abatement costs model is established using the nonparametric method, and empirical results about China in 2007 are found in this paper. The two CO2 reduction strategies, maintaining the level of CO2 or reducing CO2 and expanding GDP at the same time, impact potential GDP greatly. 143.5 millions CO2 reduction means 35.1billions GDP loss and the marginal abatement cost of CO2 is 475.3yuan/ton on average

Analyzing And Modelling Sewage Discharge Process Of Typical Area Using Time Series Analysis Method

This study is conducted to develop a mathematical model for typical sewage discharge area like residential area, commercial district and institutional area. An approach of time series analysis is applied to build the model involving model selection, parameter estimation, simulation and prediction. The description of sewage discharge process is divided into two parts: Periodic change and stationary random process. Periodic change process is simulated by harmonic analysis which composites a number of trigonometric function together. Stationary random process is described using Stationary time series including six steps: stationary test of the series; calculation of autocorrelation function and partial autocorrelation function for the series; identification of model type; determination of the model order; estimation of model parameters; verification of the model. In this paper daily variation process models for Sewage discharge of residential areas are built using this method. The numerical results show that the present method is effective and produce good agreements with the measured curve. Sewage discharge simulation of other areas like commercial area or institutional area could take the same way. This model could be used as a tool for uncertainty analysis of sewage discharge predicting. And the model also could be coupled with pipe flow model like SWMM to build sewage discharge analysis system in urban scale