Theoretical Statistics and Mathematics Unit, ISI Delhi

On Estimating the State of a Finite Level Quantum System

by 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[7] in 1989 and later investigated by S. Bandyopadhyay et al [3] in 2001 and A. O. Pittenger and M. H. Rubin [6] 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.

isid/ms/2004/17 [fulltext]

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