New Tales of the Mean King
<|reference_start|>New Tales of the Mean King: The Mean King's problem asks to determine the outcome of a measurement that is randomly selected from a set of complementary observables. We review this problem and offer a combinatorial solution. More generally, we show that whenever an affine resolvable design exists, then a state reconstruction problem similar to the Mean King's problem can be defined and solved. As an application of this general framework we consider a problem involving three qubits in which the outcome of nine different measurements can be determined without using ancillary qubits. The solution is based on a measurement derived from Hadamard designs.<|reference_end|>
@article{klappenecker2005new,
    title={New Tales of the Mean King},
    author={Andreas Klappenecker (Texas A&M University) and Martin Roetteler (NEC
  Laboratories America, Inc.)},
    journal={arXiv preprint arXiv:quant-ph/0502138},
    year={2005},
    archivePrefix={arXiv},
    eprint={quant-ph/0502138},
    primaryClass={quant-ph cs.ET}
}