Publications and Preprints
On Estimating the State of a Finite Level Quantum System
K. R. Parthasarathy
We revisit the problem of mutually unbiased measurements in the context of estimating the unknown state of a $d$-level quantum system, first studied by W. K. Wootters and B. D. fields in 1989 and later investigated by S. Bandyopadhyay et al  in 2001 and A. O. Pittenger and M. H. Rubin  in 2003. Our approach is based directly on the Weyl operators in the $L^2$-space over a finite field when $d=p^r$ 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.
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