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.