量子弱测量与信号放大

Using the strategy of weak measurements, the signals of the measuring device can be amplified significantly when the coupling strength between the quantum system and the measuring device is very weak. The significantly amplified signals could effectively reduce the relative system errors, and the weak measurement methods are very useful in improving the measuring precision in actual experiments. The widely used weak measurement formalism is introduced by Aharonov, Albert, and Vaidman(AAV), and in the AAV's formalism the measuring readings are determined by a quantity named weak value. Though the AAV's formalism is general and calculated easily, the shifts of the measuring device given by the AAV's formalism are not always valid even if the coupling strength is very weak. The upper bounds of the pointer shifts can not be derived by the AAV's formalism. In this project, without the weak value and any approximation, by studying several typical weak measurement models, the precise analytical expressions of the pointer shifts' expectation values are derived. Based on the expressions, we will theoretically pursue the maximum amplification of the signals obtained in weak measurements, and explore the weak measurements' applications in quantum information. Considering the properties of the quantum measurements in quantum information, the measuring devices with discrete levels should be mainly studied. The influence of the noise induced by the environment should be considered, the relationship between the measuring precision and the strength of the environment noise will be studied. The relationship between the maximum amplification and the pure degree of the preseletion state will be given. The implementation of this project will improve the weak measurement theory, and promote the applications of weak measurements in the actual experiments.

利用量子弱测量方案，在测量仪器和待测系统耦合强度非常弱的条件下，能够显著提高测量信号的强度，这使得弱测量方法在提高测量精度方面有着广阔的应用前景。然而现有的弱测量理论几乎都是弱值为核心，通过取近似获得的，虽然结论普适，计算简单，但是不能给出测量信号强度的极大值，无法得到弱测量提高测量精度的理论极限。本项目拟通过研究几类典型的弱测量过程，采用非弱值的、不取近似的分析方法，推导测量信号期望值精确实用的解析表达式。在此基础上，理论上找出与传统测量相比弱测量信号强度的放大上限，探索量子弱测量方案提高测量精度的极限。结合量子信息领域中量子测量的特点，重点研究文献中较少讨论的测量仪器能级为分立态的弱测量过程，探讨在有外界环境噪声干扰待测系统的情况下对利用弱测量提高测量精度的影响，及如何有效削弱噪声带来的影响。本项目的成功实施将对完善弱测量理论,推动弱测量在实验中的应用有着重要的理论指导意义。

量子测量问题在量子信息和量子计算理论中占有很重要的地位。引入后选择方案的量子弱测量理论在提高量子测量精度和解决量子基本问题方面有很重要的应用。本项目主要对弱测量理论中的放大上限，极大值受外界噪声的影响，弱测量理论在量子态和量子过程层析的应用进行研究。通过研究，我们首先得到对于任意量子态，弱测量中仪器的最大读数，以及获取极大值的条件。我们可以通过选取合适的先后选择态来获取最大的读数，以达到提高测量精度的目的。其次我们讨论了外界噪声对测量极大值的影响，发现相位阻尼和退相干的噪声能大大降低弱测量的放大效应；而对于振幅阻尼的噪声，我们则可以通过选取合适的先后选择态获取与无噪声情况下相当的放大效应。再者我们通过采用与耦合强度相关的测量仪器可观测量，在不使用近似的情况下获得弱值，对现有的利用弱值进行量子态和量子过程估计的方案进行了改进。改进后的量子态估计方案对于任意强度的测量都成立。通过寻求最小的估计态随机误差，我们又获取了最优的测量强度。在使用最优测量强度的情况下，改进后的量子态和量子过程估计方案的测量效率大大提高，并且不存在无法消除的系统误差。最后我们研究了量子测量中的负概率，利用信息理论解释了负概率产生的原因。本项目的研究成果在提高量子测量精度，实现高效的量子态和量子过程层析方面有一定的应用前景，对量子测量理论的解释也有一定的促进意义。