Abstract Certain classical codes can be viewed isomorphically as ideals of group algebras, while studying their algebraic structures help extracting the code properties. Research has shown that this was remarkably efficient in the case when the code generators are idempotents. In quantum error correction, the theory of stabilizer formalism requires classical self-orthogonal additive codes over the finite field GF(4), which, via the lens of group algebras, are essentially F2 F 2 -submodules over GF(4). Therefore, this paper provides a classification on idempotents in commutative group algebra GF(4)G, followed by a criterion that allows idempotents to generate stabilizer subgroups. Later, the construction of quantum stabilizer codes is done in the case when G is a cyclic group Cn C n , for n=2m−1 n = 2 m - 1 and n=2m+1 n = 2 m + 1 . Quantum bounds on their burst error minimum distance are subsequently determined.
Random access codes are a type of communication task that is widely used in quantum information science. The optimal average success probability that can be achieved through classical strategies is known for any random access code. However, only a few cases are solved exactly for quantum random access codes. In this paper, we provide bounds for the fully general setting of n independent variables, each selected from a d-dimensional classical alphabet and encoded in a D-dimensional quantum system subject to an arbitrary quantum measurement. The bound recovers the exactly known special cases, and we demonstrate numerically that even though the bound is not tight overall, it can still yield a good approximation.