On the Number of Elements Needed in a POVM Attaining the Accessible Information
Quantum Physics
2007-05-23 v1
Abstract
We investigate a symmetric set of three quantum states in three dimensions having interesting properties, which we call the lifted trine states. We show that for the ensemble consisting of the three lifted trine states taken with equal probabilities, the POVM measurement realizing the accessible information must contain six projectors, giving a counterexample to a conjecture of Levitin.
Cite
@article{arxiv.quant-ph/0009077,
title = {On the Number of Elements Needed in a POVM Attaining the Accessible Information},
author = {Peter W. Shor},
journal= {arXiv preprint arXiv:quant-ph/0009077},
year = {2007}
}
Comments
Will appear in Proceedings of QCM&C 2000 (Kluwer). Eventually, I plan to write a longer paper on these lifted trine states which will contain this paper as its first section