L\"uders' and quantum Jeffrey's rules as entropic projections
Quantum Physics
2014-08-18 v1 Information Theory
Mathematical Physics
math.IT
math.MP
Abstract
We prove that the standard quantum mechanical description of a quantum state change due to measurement, given by Lueders' rules, is a special case of the constrained maximisation of a quantum relative entropy functional. This result is a quantum analogue of the derivation of the Bayes--Laplace rule as a special case of the constrained maximisation of relative entropy. The proof is provided for the Umegaki relative entropy of density operators over a Hilbert space as well as for the Araki relative entropy of normal states over a W*-algebra. We also introduce a quantum analogue of Jeffrey's rule, derive it in the same way as above, and discuss the meaning of these results for quantum bayesianism.
Cite
@article{arxiv.1408.3502,
title = {L\"uders' and quantum Jeffrey's rules as entropic projections},
author = {Ryszard Paweł Kostecki},
journal= {arXiv preprint arXiv:1408.3502},
year = {2014}
}