Invariants of the local Clifford group

Maarten Van den Nest, Jeroen Dehaene, Bart De Moor
2005 Physical Review A. Atomic, Molecular, and Optical Physics  
We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct bases for these vector spaces for each degree, thereby obtaining a generating set of polynomial invariants. Our approach is based on the description of Clifford operators in terms of linear operations over GF(2). Such a study of polynomial invariants of the
more » ... cal Clifford group is mainly of importance in quantum coding theory, in particular in the classification of binary quantum codes. Some applications in entanglement theory and quantum computing are briefly discussed as well.
doi:10.1103/physreva.71.022310 fatcat:itshwjsoobdwvand6sxqxyqtcq