1304.3925 (Isaac H. Kim)

Long-range entanglement is necessary for a topological storage of
quantum information    [PDF]

Isaac H. Kim

We ask whether the ground state entanglement of a quantum many-body system imposes a fundamental constraint on its information storage capacity. We show that the amount of long-range entanglement gives a rigorous upper bound to this problem, even without invoking the properties of the parent Hamiltonian. In particular, we show that $\log N \leq 2\gamma$ for a large class of topologically ordered systems on a torus, where $N$ is the number of topologically protected states and $\gamma$ is the topological entanglement entropy. We also obtain a necessary condition for a quantum error correcting code to have a nonvanishing rate: its average entanglement entropy over the subsystems smaller than the code distance must satisfy a strict volume law.

View original: http://arxiv.org/abs/1304.3925