Quantum Lunch: Tradeoff bounds for local error correction

Abstract: Classical and quantum error correcting codes are often characterized by three parameters [n,k,d], where n is the number of physical (qu)bits, k is the number of encoded (qu)bits, and d is the code distance (i.e. the minimal number of (qu)bits required to reveal information about an encoded state). The (quantum) error correcting codes can themselves be defined in a number of different ways. We consider codes defined as the ground subspace of a set of local projectors on a lattice. If the projectors are commuting, then the following bound can be show for quantum codes: kd^2<= O(n) on a 2D lattice. If the projectors are non-commuting, then the bound kd<=O(n) can be shown on a 2D lattice. In both cases, examples exist saturating the bounds. If time permits, I will talk about extending these results to approximate error correcting codes.