 
Summary: Solution to the King's Problem in Prime Power Dimensions
P. K. Aravind
Physics Department, Worcester Polytechnic Institute, Worcester, MA 01609, U. S.A.
Reprint requests to Prof. P.K. A.; Email: paravind@wpi.edu
Z. Naturforsch. 58a, 85 92 (2003); received November 5, 2002
It is shown how to ascertain the values of a complete set of mutually complementary observables of
a prime power degree of freedom by generalizing the solution in prime dimensions given by Englert
and Aharonov [Phys. Lett. A284, 1 5 (2001)].
Key words: Mutually Unbiased Bases; King's Problem; Quantum State Estimation.
1. Introduction
The King's Problem [1] is the following: A physi
cist is trapped on an island ruled by a mean king who
promises to set her free if she can give him the an
swer to the following puzzle. The physicist is asked to
prepare a dstate quantum system in any state of her
choosing and give it to the king, who measures one
of several sets of mutually unbiased observables (this
term will be defined below) on it. Following this, the
physicist is allowed to make a control measurement on
the system, as well as any other systems it may have
