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An Area Law for One Dimensional Quantum Systems
We prove an area law for the entanglement entropy in gapped one-dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in termsExpand
Superadditivity of communication capacity using entangled inputs
The additivity conjecture of quantum information theory implies that entanglement cannot, even in principle, help to funnel more classical information through a quantum-communication channel. AExpand
Spectral Gap and Exponential Decay of Correlations
We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wideExpand
Progress towards practical quantum variational algorithms
The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and theExpand
Lieb-Robinson bounds and the generation of correlations and topological quantum order.
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails.Expand
Towards the fast scrambling conjecture
A bstractMany proposed quantum mechanical models of black holes include highly non-local interactions. The time required for thermalization to occur in such models should reflect the relaxation timesExpand
Area laws in quantum systems: mutual information and correlations.
This Letter shows that the holographic principle not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. Expand
Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance
We define for quantum many-body systems a quasiadiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy densityExpand
Laplacian growth as one-dimensional turbulence
Abstract A new model of Laplacian stochastic growth is formulated using conformal mappings. The model describes two growth regimes, stable and turbulent, separated by a sharp phase transition. TheExpand
Topological quantum order: Stability under local perturbations
We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum ofExpand