LongRange Entanglement Is Necessary for a Topological Storage of Quantum Information
Abstract
A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum state ψ⟩, we obtain an upper bound on the number of distinct states that are locally indistinguishable from ψ⟩. The upper bound is determined only by the entanglement entropy of some local subsystems. As an example, we show that logN≤2γ for a large class of topologically ordered systems on a torus, where N is the number of topologically protected states and γ is the constant subcorrection term of the entanglement entropy. We discuss applications to quantum manybody systems that do not have any lowenergy topological quantum field theory description, as well as tradeoff bounds for general quantum error correcting codes.
 Publication:

Physical Review Letters
 Pub Date:
 August 2013
 DOI:
 10.1103/PhysRevLett.111.080503
 arXiv:
 arXiv:1304.3925
 Bibcode:
 2013PhRvL.111h0503K
 Keywords:

 03.67.Pp;
 03.65.Ud;
 03.67.Ac;
 73.43.f;
 Quantum error correction and other methods for protection against decoherence;
 Entanglement and quantum nonlocality;
 Quantum algorithms protocols and simulations;
 Quantum Hall effects;
 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 5 pages, 1 figure, minor changes. For more details, see the first version. After submitting this work to the journal, I have found a related work by T. Osborne