No abstract

We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a fixed rate of inconclusive results. Our approach can deal with any problem in which each of the objective and constraint functions is formulated by the sum of the traces of the multiplication of a Hermitian operator and a detection operator. We first derive dual problems and necessary and sufficient conditions for an optimal measurement. We also consider the minimax version of these problems and provide necessary and sufficient conditions for a minimax solution. Finally, for optimization problem having a certain symmetry, there exists an optimal solution with the same symmetry. Examples are shown to illustrate how our results can be used

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Large pore defects clearly develop in Al 2 O 3 ceramics during sintering. These large pores originate from voids caused by the incomplete deformation and adhesion of powder particles in collapsed dimples at the centers and boundaries of granules in the green compacts. The coalescence of pores, with limited shrinkage, during densification and grain growth in the late intermediate to final stages of sintering, is considered responsible for the development of the large pores. The mechanism of pore coalescence is explained by thermodynamic arguments, which demonstrate that the largest pores result in a stable system.