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Updated: May 8, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Long-range entanglement is necessary for a topological storage of quantum information
1Institute of Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA.
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 log N≤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 many-body systems that do not have any low-energy topological quantum field theory description, as well as tradeoff bounds for general quantum error correcting codes.
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