On Estimating the State of a Finite Level Quantum System

2004/08/11 by K. R. Parthasarathy, Parthasarathy, K. R.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0408069

arxiv created 2004/08/11 · arxiv updated 2009/12/01

Abstract

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 L²-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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