Symmetric Informationally Complete Quantum Measurements
Quantum Physics
2007-07-16 v1 Information Theory
Functional Analysis
math.IT
Abstract
We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal. Such a set is called a ``symmetric, informationally complete'' POVM (SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d. SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions two, three, and four. We further conjecture that a particular kind of group-covariant SIC-POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.
Cite
@article{arxiv.quant-ph/0310075,
title = {Symmetric Informationally Complete Quantum Measurements},
author = {Joseph M. Renes and Robin Blume-Kohout and A. J. Scott and Carlton M. Caves},
journal= {arXiv preprint arXiv:quant-ph/0310075},
year = {2007}
}
Comments
8 pages