Prior Information: How to Circumvent the Standard Joint-Measurement Uncertainty Relation

Abstract

The use of prior information in order to avoid the standard joint-measurement uncertainty relation, was discussed. It was shown that with the same physical experimental setup and knowledge of the system density prior to measurement, the improved joint estimates were obtained. The overlap uncertainty principle pointed towards the existence of nonorthogonal states and showed that the quantum states occupy a phase-space area of at least 2πℏ. The results show that by using prior information about the system , the standard uncertainty relation for the canonical joint measurement of position and momentum can be improved up to a factor of 4. Show more