Universally Fisher-Symmetric Informationally Complete Measurements

Understand

A quantum measurement is Fisher symmetric if it provides uniform and maximal information on all parameters that characterize the quantum state of interest.

• Using (complex projective) 2-designs, we construct measurements on a pair of identically prepared quantum states that are Fisher symmetric for all pure states.
• Such measurements are optimal in achieving the minimal statistical error without adaptive measurements.
• We then determine all collective measurements on a pair that are Fisher symmetric for the completely mixed state and for all pure states simultaneously.