Deformations of the symmetric subspace of qubit chains

Abstract: The symmetric subspace of multi-qubit systems, that is, the space of states invariant under permutations, is commonly encountered in applications in the context of quantum information and communication theory. It is known that the symmetric subspace can be described in terms of irreducible representations of the group $SU(2)$, whose representation spaces form a basis of symmetric states, the so-called Dicke states. In this work, we present deformations of the symmetric subspace as deformations of this group structure, which are promoted to a quantum group $\mathcal{U}_q(\mathfrak{su}(2))$. We see that deformations of the symmetric subspace obtained in this manner correspond to local deformations of the inner product of each spin, in such a way that departure from symmetry can be encoded in a position-dependent inner product. The consequences and possible extensions of these results are also discussed.