Dr. Isaac Kim - The Perimeter Institute: An inequality between entanglement entropy and a number of encoded qubits

Abstract:

Entanglement entropy is a canonical measure for quantifying
entanglement in a bipartite system. In this talk, I will show that a
suitable linear combination of entanglement entropy gives a natural upper
bound to the number of qubits that can be reliably encoded in a system. We
discuss applications of this inequality to gapped quantum many-body
systems that do not necessarily have a low-energy topological quantum
field theory description, as well as tradeoff bounds for general quantum
error correcting codes. Several open problems in this direction shall be
discussed as well.