Precision Optical Measurements Using Weak Values and Nonclassical State

We consider a number of optical precision measurement schemes, and their statistical performance. We place a particular emphasis on the performance of several enhancements to weak value measurements in optical displacement and deflection measurements. In particular, to overcome losses to "postselection'' present in any weak value measurement, we examine two separate "recycling'' schemes which allow each photon to have many chances of being postselected. We also show that this type of weak value measurement is capable of being used in conjunction with squeezed states of light, allowing for substantial reductions in quantum uncertainty of (say) the position of a an optical beam while also reducing the effects of technical noise. Finally, we examine a simple scheme for using entangled biphoton pairs to approximately achieve Heisenberg scaling in an optical displacement measurement.