Long-range entanglement is necessary for a topological storage of quantum information - INSPIRE

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

Isaac H. Kim
(
- Caltech, IQI
)

Apr 14, 2013

5 pages

Published in:

Phys.Rev.Lett. 111 (2013) 080503

Published: Aug 23, 2013

e-Print:

1304.3925 [quant-ph]

DOI:

10.1103/PhysRevLett.111.080503

View in:

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Abstract: (APS)

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.

Note:

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; see arXiv:0806.2962

03.67.Pp
03.65.Ud
03.67.Ac
73.43.-f

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Figures(1)

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