Lieb-Robinson bounds and the generation of correlations and topological quantum order

Abstract

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. We discuss several consequences of this result in the context of quantum information theory. First, we show that the information that leaks out to space-like separated regions is negligable, and that there is a finite speed at which correlations and entanglement can be distributed. Second, we discuss how these ideas can be used to prove lower bounds on the time it takes to convert states without topological quantum order to states with that property. Finally, we show that the rate at which entropy can be created in a block of spins scales like the boundary of that block.

arXiv commentSee also Eisert and Osborne, quant-ph/0603114

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• Optimal Local Measurements in Single-Parameter Quantum Metrology
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• No eigenstate of the critical transverse-field Ising chain satisfies the area law
• Signatures of quantum chaos and complexity in the Ising model on random graphs
• Ballistic propagation of a local impact in the one-dimensional $XY$ model
• Geometrically Taming Dynamical Entanglement Growth in Purified Quantum States
• Suppression of the horizon effect in pairing correlation functions of $t$-$J$ chains after a quantum quench
• Macroscopic Quantum States and Universal Correlations in a Disorder-Order Interface Propagating over a 1D Ground State
• Light Cones in Classical Dipole-Dipole Interacting Systems
• Instantaneous measurement can isolate the information
• Emergent quantum field theories on curved spacetimes in spinor Bose-Einstein condensates: from scalar to Proca fields
• Clustering of steady-state correlations in open systems with long-range interactions
• Emergence of caustics in dynamics of the Kitaev model
• Topological order on the Bloch sphere
• Towards a Geometrization of Quantum Complexity and Chaos
• Entanglement transition in a cluster spin chain coupled with free spins
• Non-Equilibrium Quantum Many-Body Physics with Quantum Circuits
• Unfolding the Toric Code Model with Emergent Qubits
• Floquet-engineered system-reservoir interaction in the transverse field Ising model
• Locally accurate tensor networks for thermal states and time evolution
• Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains
• Error bounds on the universal Lindblad equation in the thermodynamic limit
• Multipartite Entanglement in Crossing the Quantum Critical Point
• Theoretical study on thermalization in isolated quantum systems
• Quantum Information Approaches to Quantum Gravity
• A Shielding Property for Thermal Equilibrium States on the Quantum Ising Model
• Symmetry resolved out-of-time-order correlators of Heisenberg spin chains using projected matrix product operators
• Quantum wake dynamics in Heisenberg antiferromagnetic chains