While for non-relativistic short-range interactions, the spread of information is local, remaining confined in an effective light cone, long-range interactions can generate either nonlocal (faster-than-ballistic) or local (ballistic) spread of correlations depending on the initial conditions. This makes long-range interactions a rich platform for controlling the spread of information. Here, we derive an effective Hamiltonian analytically and identify the specific interaction term that drives nonlocality in a wide class of long-range spin chains. This allows us to understand the conditions for the emergence of local behavior in the presence of nonlocal interactions and to identify a regime where the causal space-time landscape can be precisely designed. Indeed, we show that for large long-range interaction strength or large system size, initial conditions can be chosen in a way that allows a local perturbation to generate nonlocal signals at programmable distant positions, which then propagate within effective light cones. The possibility of engineering the emergence of nonlocal Lieb-Robinson-like light cones allows one to shape the causal landscape of long-range interacting systems, with direct applications to quantum information processing devices, quantum memories, error correction, and information transport in programmable quantum simulators.
While for non-relativistic short-range interactions, the spread of information is local, remaining confined in an effective light cone, long-range interactions can generate either nonlocal (faster-than-ballistic) or local (ballistic) spread of correlations depending on the initial conditions. This makes long-range interactions a rich platform for controlling the spread of information. Here, we derive an effective Hamiltonian analytically and identify the specific interaction term that drives nonlocality in a wide class of long-range spin chains. This allows us to understand the conditions for the emergence of local behavior in the presence of nonlocal interactions and to identify a regime where the causal space-time landscape can be precisely designed. Indeed, we show that for large long-range interaction strength or large system size, initial conditions can be chosen in a way that allows a local perturbation to generate nonlocal signals at programmable distant positions, which then propagate within effective light cones. The possibility of engineering the emergence of nonlocal Lieb-Robinson-like light cones allows one to shape the causal landscape of long-range interacting systems, with direct applications to quantum information processing devices, quantum memories, error correction, and information transport in programmable quantum simulators.
Locality imposes stringent constraints on the spreading of information in nonrelativistic quantum systems, which is reminiscent of a ``light cone,'' a causal structure arising in their relativistic counterparts. Long-range interactions can potentially soften such constraints, allowing almost instantaneous long jumps of particles, into the ``spacelike'' region, thus defying causality. Since interactions decaying as a power law with distance ${r}^{\ensuremath{-}\ensuremath{\alpha}}$ are ubiquitous in nature, it is pertinent to understand what is the fate of causality and information spreading in such systems. Using a numerically exact technique we address these questions by studying the out-of-time-order correlation function of a representative generic system in one dimension. We show that while the interactions are long range, their effect on information spreading is asymptotically negligible as long as $\ensuremath{\alpha}>1$. In this range we find a complex compound behavior, where, after a short transient, a fully local behavior emerges, yielding asymptotic light cones virtually indistinguishable from light cones in corresponding local models. The long-range nature of the interaction is only expressed in the power-law leaking of information from the light cone, with the same exponent as the exponent of the interaction $\ensuremath{\alpha}$. Our results directly apply also to corresponding response functions and suggest that previously obtained rigorous bounds on information spreading in long-range interacting systems are not tight, and could be potentially improved.
This preprint clarifies a persistent category error in the interpretation of quantum mechanics and relativity by explicitly distinguishing propagation from correlation. Relativistic constraints, including the finite speed of light, apply to the transmission of energy, matter, and information through spacetime. Quantum mechanics, by contrast, permits nonlocal correlations between entangled systems that do not involve transmission, motion, or signal propagation. The apparent instantaneity of quantum effects therefore reflects the revelation of pre-existing correlation structure rather than superluminal dynamics. By maintaining this separation, the preprint shows that the finite speed of light and quantum nonlocality are not in conflict. Light is limited in speed because it propagates; quantum correlations have no speed because nothing propagates. This framing resolves common misconceptions surrounding entanglement, nonlocality, and causality without introducing hidden structures, preferred frames, or violations of relativistic invariance. The work is intended as a conceptual clarification and falsifiable interpretive framework, not a modification of quantum theory or relativity. Keywords quantum correlation nonlocality entanglement speed of light relativity causality non-signaling propagation vs correlation foundations of quantum mechanics conceptual clarification
Scalable quantum networks require processing nodes with flexible internal connectivity, yet neutral-atom architectures remain constrained by the strong spatial dependence of native Rydberg interactions. Here we show that a Rydberg atom chain can act as a coherent quantum bus, converting a locally connected one-dimensional architecture into an effectively nonlocal interaction network. Virtual excitations in the dispersive regime mediate controllable interactions between spatially separated data units, which we derive analytically using a Green's-function continued-fraction method. The resulting mechanism is not restricted to single-excitation dynamics and supports several distinct functionalities, including Floquet-engineered chiral transport, remote entanglement of mechanical oscillators, and destructive interference for selectively suppressing unwanted dipole exchange. Simulations incorporating full long-range Rydberg interactions, atomic position fluctuations, and finite Rydberg-state lifetimes show that the mediated dynamics remain robust under experimentally relevant conditions. These results establish Rydberg chains as programmable coherent mediators for extending the internal connectivity of neutral-atom quantum nodes toward quasi-all-to-all coupling, providing a hardware-level route toward scalable and reconfigurable quantum-network architectures.
Memory effects in many-body quantum systems interacting with an environment significantly impact their behavior. Nevertheless, much of our understanding of many-body open quantum systems is based on models within the Born-Markov approximation where these effects are neglected. In this paper, we consider a general class of spatially local open quantum lattice models with a non-Markovian environment that is approximated as Gaussian. Our main result is a set of Lieb-Robinson bounds for such models. For models where the environment has independent local baths, we show that the Lieb-Robinson velocity is controlled by one-norm of the memory kernel within the evolution time-interval, yielding a linear light cone whenever the memory kernel has a bounded one-norm. For models where excitations can propagate through the environment, we prove a polynomial light cone that captures bath-mediated acceleration of information spreading. In both of these cases, we show that the derived Lieb-Robinson bounds are tight by also constructing lattice models saturating these bounds. Finally, we consider the problem of approximating a non-Markovian model by a larger Markovian model, which contains the system spins together with only a finite number of bosonic environment modes. We establish that as a consequence of our Lieb-Robinson bounds, the number of environment modes {per system site} needed to accurately capture local observables is independent of the size of the system.
In nonrelativistic quantum theories with short-range Hamiltonians, a velocity v can be chosen such that the influence of any local perturbation is approximately confined to within a distance r until a time $t\ensuremath{\sim}r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/{r}^{\ensuremath{\alpha}}$) interactions, when $\ensuremath{\alpha}$ exceeds the dimension D, an analogous bound confines influences to within a distance r only until a time $t\ensuremath{\sim}(\ensuremath{\alpha}/v)\mathrm{log}r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are bounded by a polynomial for $\ensuremath{\alpha}>2D$ and become linear as $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems.
The nonequilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address this issue by analyzing a local quantum quench in the long-range Ising model in a transverse field, where interactions decay as a variable power law with distance ∝r(-α), α>0. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for α>2, weakly long range for 1<α<2 without a clear light cone but with a finite propagation speed of almost all excitations, and fully nonlocal for α<1 with instantaneous transmission of correlations. This last regime breaks generalized Lieb-Robinson bounds and thus locality. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasiparticles remains valid, allowing an intuitive interpretation of our findings via divergences of quasiparticle velocities. Our results may be tested in state-of-the-art trapped-ion experiments.