Zero-Error Capacity and Invariant Subspace of a Quantum Channel

In this paper, we explore the connection between the zero-error capacity and the invariant subspace of a quantum channel. We begin by demonstrating that a quantum channel with two invariant subspaces, which only have trivial intersections, has a positive zero-error capacity. Additionally, we establish that an unital quantum channel with a non-trivial invariant subspace of at least two dimensions also has a positive zero-error capacity.