Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, a novel quantum detector tomography method is proposed. First, a series of different probe states are used to generate measurement data. Then, using constrained linear regression estimation, a stage-1 estimation of the detector is obtained. Finally, the positive semidefinite requirement is added to guarantee a physical stage-2 estimation. This Two-stage Estimation (TSE) method has computational complexity O(nd2M), where n is the number of d-dimensional detector matrices and M is the number of different probe states. An error upper bound is established, and optimization on the coherent probe states is investigated. We perform simulation and a quantum optical experiment to testify the effectiveness of the TSE method.

The efficiency of real-time digital image processing operations has an important impact on the cost and realizability of complex algorithms. Global motion estimation is an example of such a complex algorithm. Most digital image processing is carried out with a precision of 8 bits per pixel, however there has always been interest in low-complexity algorithms. One way of achieving low complexity is through low precision, such as might be achieved by quantization of each pixel to a single bit. Previous approaches to one-bit motion estimation have achieved quantization through a combination of spatial filtering/averaging and threshold setting. In this paper we present a generalized framework for precision reduction. Motivated by this framework, we show that bit-plane selection provides higher performance, with lower complexity, than conventional approaches to quantization.