ON ESTIMATING THE STATE OF A FINITE LEVEL QUANTUM SYSTEM
Kalyanapuram Rangachari Parthasarathy · Infinite Dimensional Analysis Quantum Probability and Related Topics · 2004
We revisit the problem of mutually unbiased measurements in the context of estimating the unknown state of a d-level quantum system, first studied (in the framework of quantum information) by Wootters and fields7 in 1989 and later investigated by Bandyopadhyay et al.3 in 2001 and Pittenger and Rubin6 in 2003. Our approach is based directly on the Weyl operators in the L2-space over a finite field when d=pr is the power of a prime. When d is not a prime power we sacrifice a bit of optimality and construct a recovery operator for reconstructing the unknown state from the probabilities of elementary events in different measurements.