Physics – Quantum Physics
Scientific paper
2011-09-26
Physics
Quantum Physics
Scientific paper
We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify a quantum system which is constrained by prior information? We show that if the prior information restricts the system to a set of lower dimensionality, then topological obstructions can increase the required number of outcomes by a factor of two over the number of real parameters needed to characterize the system. Conversely, we show that almost every measurement becomes informationally complete with respect to the constrained set if the number of outcomes exceeds twice the Minkowski dimension of the set. We apply the obtained results to determine the minimal number of outcomes of measurements which are informationally complete with respect to states with rank constraints. In particular, we show that 4d-4 measurement outcomes (POVM elements) is enough in order to identify all pure states in a d-dimensional Hilbert space, and that the minimal number is at most 2 log_2(d) smaller than this upper bound.
Heinosaari Teiko
Mazzarella Luca
Wolf Michael M.
No associations
LandOfFree
Quantum Tomography under Prior Information does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum Tomography under Prior Information, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Tomography under Prior Information will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-688498