In a locally interacting many-body system, two isolated qubits, separated by a large distance r, become correlated and entangled with each other at a time t ≥ r/v [1]. This finite speed v of quantum information scrambling limits quantum information processing [2], thermalization [3] and even equilibrium correlations [4]. Yet most experimental systems contain long range power law interactions -qubits separated by r have potential energy V (r) ∝ r −α . Examples include the long range Coulomb interactions in plasma (α = 1) and dipolar interactions between spins (α = 3). In one spatial dimension, we prove that the speed of quantum scrambling remains finite for sufficiently large α. This result parametrically improves previous bounds [4][5][6][7], compares favorably with recent numerical simulations [8,9], and can be realized in quantum simulators with dipolar interactions [10,11]. Our new mathematical methods lead to improved algorithms for classically simulating quantum systems [6,12], and improve bounds on environmental decoherence in experimental quantum information processors.Almost five decades ago, Lieb and Robinson proved that spatial locality implies the ballistic propagation of quantum information [1]. Intuitively defining a "scrambling time" t s (r) by the time at which an initially isolated qubit can significantly entangle with another a distance r away, locality implies that t s (r)r. This result has deep implications in theoretical physics: emergent spacetime locality arising from microscopic quantum mechanics without manifest relativistic invariance may play a crucial role in understanding quantum gravity through the holographic correspondence [13]. Moreover, if quantum information can only propagate with a finite speed, a classical computer can efficiently approximate early time quantum dynamics [12], and a quantum information processor with short-range interactions cannot become entangled with an infinite environment arbitrarily quickly [14,15], despite the exponentially large Hilbert space in many-body quantum systems.While the Lieb-Robinson theorem is quite elegant, it is not useful for a typical quantum information processor. A qubit in an experimental device is usually a spin or atomic degree of freedom, or Josephson junction. Such objects generically interact with long range interactions, and until now, whether locality of quantum scrambling necessarily persists in the presence of long range interactions has remained unclear. In 2005, Hastings and Koma used the canonical Lieb-Robinson theorem to prove that when α > d, t s (r) log r [4]; more recently, this bound has been improved for α > 2d to t s (r) r (α−2d)/(α−d) [6]. If such bounds were tight, then insulating a quantum processor from its environment would be absolutely crucial. Yet numerical simulations cast into doubt the tightness of these formal bounds: two groups have recently shown that t s r in one dimensional models with α 1.8 [8] or even α > 1 [9], depending on microscopic details.In this letter, we prove that t s (r) r whenever α > 3...

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. Local operations at sufficiently separated spacetime points approximately commute-given a many-body state jψi, O x ðtÞO y jψi ≈ O y O x ðtÞjψi with arbitrarily small errors-so long as jx − yj ≳ vt, where v is finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distance r interact with potential energy VðrÞ ∝ 1=r α. 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, this linear light cone exists for every many-body state jψi when α > 3 (Lieb-Robinson light cone); for a typical state jψi chosen uniformly at random from the Hilbert space when α > 5 2 (Frobenius light cone); and for every state of a noninteracting system 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 universal quantum state transfer, as well as manybody quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.

At the heart of recent progress in AdS/CFT is the question of subregion duality, or entanglement wedge reconstruction: which part(s) of the boundary CFT are dual to a given subregion of the bulk? This question can be answered by appealing to the quantum error correcting properties of holography, and it was recently shown that robust bulk (entanglement wedge) reconstruction can be achieved using a universal recovery channel known as the twirled Petz map. In short, one can use the twirled Petz map to recover bulk data from a subset of the boundary. However, this map involves an averaging procedure over bulk and boundary modular time, and hence it can be somewhat intractable to evaluate in practice. We show that a much simpler channel, the Petz map, is sufficient for entanglement wedge reconstruction for any code space of fixed finite dimension -no twirling is required. Moreover, the error in the reconstruction will always be non-perturbatively small. From a quantum information perspective, we prove a general theorem extending the use of the Petz map as a general-purpose recovery channel to subsystem and operator algebra quantum error correction.