TY - JOUR T1 - The Lieb-Robinson light cone for power-law interactions Y1 - 2021 A1 - Minh C. Tran A1 - Andrew Y. Guo A1 - Christopher L. Baldwin A1 - Adam Ehrenberg A1 - Alexey V. Gorshkov A1 - Andrew Lucas AB -

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/rα at distance r? Here, we present a definitive answer to this question for all exponents α>2d and all spatial dimensions d. Schematically, information takes time at least rmin{1,α−2d} to propagate a distance~r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

UR - https://arxiv.org/abs/2103.15828 ER - TY - JOUR T1 - Hierarchy of linear light cones with long-range interactions JF - Physical Review X Y1 - 2020 A1 - Minh C. Tran A1 - Chi-Fang Chen A1 - Adam Ehrenberg A1 - Andrew Y. Guo A1 - Abhinav Deshpande A1 - Yifan Hong A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov A1 - Andrew Lucas AB -

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a "linear light cone," which expands at an emergent velocity analogous to the speed of light. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance r interact with potential energy V(r)∝1/rα. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same α, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, commutators of local operators ⟨ψ|[Ox(t),Oy]|ψ⟩ are negligible in every state |ψ⟩ when |x−y|≳vt, where v is finite when α>3 (Lieb-Robinson light cone); in a typical state |ψ⟩ drawn from the infinite temperature ensemble, v is finite when α>52 (Frobenius light cone); in non-interacting systems, v is finite in every state when α>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones, and their tightness, also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that quantum state transfer and many-body quantum chaos are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

VL - 10 UR - https://arxiv.org/abs/2001.11509 CP - 031009 U5 - https://doi.org/10.1103/PhysRevX.10.031009 ER - TY - JOUR T1 - Optimal state transfer and entanglement generation in power-law interacting systems Y1 - 2020 A1 - Minh C. Tran A1 - Abhinav Deshpande A1 - Andrew Y. Guo A1 - Andrew Lucas A1 - Alexey V. Gorshkov AB -

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law (1/rα) interactions. For all power-law exponents α between d and 2d+1, where d is the dimension of the system, the protocol yields a polynomial speedup for α>2d and a superpolynomial speedup for α≤2d, compared to the state of the art. For all α>d, the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states. 

UR - https://arxiv.org/abs/2010.02930 ER -