On the Observables Describing a Quantum Reference Frame
Abstract
A reference frame F is described by the element g of the Poincare' group P which connects F with a given fixed frame F_0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have to be considered as quantum observables. However, these observables are not compatible and some of them, namely the coordinates of the origin of F, cannot be represented by self-adjoint operators. Both these difficulties can be overcome by considering a positive-operator-valued measure (POVM) on P, covariant with respect to the left translations of the group, namely a covariance system. We develop a construction procedure for this kind of mathematical structure. The formalism is also used to discuss the quantum observables measured with respect to a quantum reference frame.
Cite
@article{arxiv.quant-ph/0006060,
title = {On the Observables Describing a Quantum Reference Frame},
author = {S. Mazzucchi},
journal= {arXiv preprint arXiv:quant-ph/0006060},
year = {2015}
}
Comments
23 pages, no figures