Abstract:

The concept of a (A,B)-quantum measurement is introduced and discussed. An equivalent relation between (A,B)-quantum measurement and g-frame with lower and upper bounds A and B is established. Some properties of direct sums and multiplications of (A,B)-quantum measurements are obtained. The measure frame operator and the dual quantum measurement of a (A,B)-quantum measurement are introduced and its canonical dual is constructed. Finally, a reconstruction formula of a quantum states is obtained in light of a (A,B)-quantum measurement.

Key words: (A,B)-quantum measurement; g-frame; measure frame operator; reconstruction formula