@article{decker2004implementation,
author = {Decker, Thomas and Janzing, Dominik and Roetteler, Martin},
title = {Implementation of Group-Covariant POVMs by Orthogonal Measurements},
year = {2004},
month = {July},
abstract = {We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark's theorem a POVM can be implemented by an orthogonal measurement on a larger system. Accordingly, our goal is to find an implementation of a given group-covariant POVM by a quantum circuit using its symmetry. Based on representation theory of the symmetry group we develop a general approach for the implementation of group-covariant POVMs which consist of rank-one operators. The construction relies on a method to decompose matrices that intertwine two representations of a finite group. We give several examples for which the resulting quantum circuits are efficient. In particular, we obtain efficient quantum circuits for a class of POVMs generated by Weyl-Heisenberg groups. These circuits allow to implement an approximative simultaneous measurement of the position and crystal momentum of a particle moving on a cyclic chain.},
url = {http://approjects.co.za/?big=en-us/research/publication/implementation-group-covariant-povms-orthogonal-measurements/},
journal = {Journal of Mathematical Physics},
volume = {46},
}