Sonia L'Innocente

Strongly Minimal Modules Over Group Rings

ABSTRACT We consider modules over a group ring RG where R is a countable Dedekind domain and G is a finite group. We describe the internal structure of those RG-modules which are strongly minimal or satisfy other related model theoretic and algebraic minimality conditions.

Quantifying the performance of quantum codes

We study the properties of error correcting codes for noise models in the presence of asymmetries and/or correlations by means of the entanglement fidelity and the code entropy. First, we consider a dephasing Markovian memory channel and characterize the performance of both a repetition code and an error avoiding code (

Exponentiations over the universal enveloping algebra of sl2(C)

\mathcal{C}_{{\rm{RC}}}

RINGS OF DEFINABLE SCALARS OF VERMA MODULES

and

Weakly minimal modules over integral group rings and over related classes of rings

\mathcal{C}_{{\rm{DFS}}}

On the decidability of the theory of modules over the ring of algebraic integers

, respectively) in terms of the entanglement fidelity. We also consider the concatenation of such codes (

Quantum state transfer in a q-deformed chain

\left( {\mathcal{C}_{{\rm{DFS}}} \, \circ \,\mathcal{C}_{{\rm{RC}}} } \right)

Minimalities and Modules over Dedekind-Like Rings

) and show that it is especially advantageous in the regime of partial correlations. Finally, we characterize the effectiveness of the codes

Factorisation of germ-like series

\mathcal{C}_{{\rm{DFS}}}

ON THE MODEL THEORY OF THE LOGARITHMIC FUNCTION IN COMPACT LIE GROUPS

,