In most probabilistic teleportation schemes, if the teleportation fails, the unknown quantum state will be completely ruined. In addition, the frequently proposed high-dimensional unitary operations are very difficult to realize experimentally. To maintain the integrity of the unknown quantum state to be teleported, this analysis does not focus attention on the original multi-particle state but seeks to construct a faithful channel with an ancillary particle and a unified high-dimensional unitary operation. The result shows that if the construction of the multi-group Einstein-Podolsky-Rosen pair succeeds, the original multi-particle state can be used to deterministically teleport the unknown quantum state of the entangled multiple particles which avoids undermining the integrity of the unknown state brought about by failure. This unified high-dimensional operation is appealing due to the obvious experimental convenience.

Nonlinear least trimmed squares (NLTS) estimator is a very important kind of nonlinear robust estimator, which is widely used for recovering an ideal high-quality signal from contaminated data. However, the NLTS estimator has not been widely used because it is hard to compute. This paper develops an algorithm to compute the NLTS estimator based on a random differential evolution (DE) strategy. The strategy which uses random DE schemes and control variables improves the DE performance. The simulation results demonstrate that the algorithm gives better performance and is more convenient than existing computing algorithms for the NLTS estimator. The algorithm makes the NLTS estimator easy to apply in practice, even for large data sets, e.g. in a data mining context.

In quantum circuits, importing of additional qubits can reduce the operation time and prevent decoherence induced by the environment. However, excessive qubits may make the quantum system vulnerable. This paper describes how to relax existing qubits without additional qubits to significantly reduce the operation time of the quantum Fourier circuit compared to a circuit without optimization. The results indicate that this scheme makes full use of the qubits relaxation. The concepts can be applied to improve similar quantum circuits and guide the physical implementations of quantum algorithms or devices.

As fractal image encoding algorithms can yield high-resolution reconstructed images at very high compression ratio, and therefore, have a great potential for improving the efficiency of image storage and image transmission. However, the baseline fractal encoding algorithm requires a great deal of time to complete the best matching search between the range and domain blocks, which greatly limits practical applications of the algorithm. In order to solve this problem, a necessary condition of the best matching search based on an image feature is proposed in this paper. The proposed method can reduce the search space significantly and excludes the most inappropriate domain blocks for each range block before carrying out the best matching search. Experimental results show that the proposed algorithm can produce good quality reconstructed images and requires much less time than the baseline encoding algorithm. Specifically, the new algorithm can speed up encoding by about 85 times with a loss of just 3 dB in the peak signal to noise ratio (PSNR), and yields compression ratios close to 34.

The fractal image encoding method has received much attention for its many advantages over other methods, such as high decoding quality at high compression ratios. However, because every range block must be compared to all domain blocks in the codebook to find the best-matched one during the coding procedure, baseline fractal coding (BFC) is quite time consuming. To speed up fractal coding, a new fast fractal encoding algorithm is proposed. This algorithm aims at reducing the size of the search window during the domain-range matching process to minimize the computational cost. A new theorem presented in this paper shows that a special feature of the image can be used to do this work. Based on this theorem, the most inappropriate domain blocks, whose features are not similar to that of the given range block, are excluded before matching. Thus, the best-matched block can be captured much more quickly than in the BFC approach. The experimental results show that the runtime of the proposed method is reduced greatly compared to the BFC method. At the same time, the new algorithm also achieves high reconstructed image quality. In addition, the method can be incorporated with other fast algorithms to achieve better performance. Therefore, the proposed algorithm has a much better application potential than BFC.