Optimal State Transfer and Entanglement Generation in Power-Law Interacting Systems

Quantum Delocalization on Correlation Landscape: The Key to Exponentially Fast Multipartite Entanglement Generation

Entanglement, a hallmark of quantum mechanics, is a vital resource for quantum technologies. Generating highly entangled multipartite states is a key goal in current quantum experiments. We unveil a novel framework for understanding entanglement generation dynamics in Hamiltonian systems by quantum delocalization of an effective operator wave function on a correlation landscape. Our framework establishes a profound connection between the exponentially fast generation of multipartite entanglement, witnessed by the quantum Fisher information, and the linearly increasing asymptotics of hopping amplitudes governing the delocalization dynamics in Krylov space. We illustrate this connection using the paradigmatic Lipkin-Meshkov-Glick model and highlight potential signatures in chaotic Feingold-Peres tops. Our results provide a transformative tool for understanding and harnessing rapid entanglement production in complex quantum systems, providing a pathway for quantum enhanced technologies by large-scale entanglement.

Strong Quantum Metrological Limit from Many-Body Physics

Surpassing the standard quantum limit and even reaching the Heisenberg limit using quantum entanglement, represents the Holy Grail of quantum metrology. However, quantum entanglement is a valuable resource that does not come without a price. The exceptional time overhead for the preparation of large-scale entangled states raises disconcerting concerns about whether the Heisenberg limit is fundamentally achievable. Here, we find a universal speed limit set by the Lieb-Robinson light cone for the quantum Fisher information growth to characterize the metrological potential of quantum resource states during their preparation. Our main result establishes a strong precision limit of quantum metrology accounting for the complexity of many-body quantum resource state preparation and reveals a fundamental constraint for reaching the Heisenberg limit in a generic many-body lattice system with bounded one-site energy. It enables us to identify the essential features of quantum many-body systems that are crucial for achieving the quantum advantage of quantum metrology, and brings an interesting connection between many-body quantum dynamics and quantum metrology.

Quantum correlation propagation in a waveguide-QED system with long-range interaction

We investigate the excitation and correlation propagations among a one-dimensional atom chain with exponentially decaying, ideal long-range, and power-law decaying interactions. We show that although a clear light-cone-like structure can appear in both the excitation and correlation propagation patterns under the exponentially decaying interaction, only an obscure light-cone-like structure appears with multi-power-law decaying interaction and surprisingly an inverse light-cone-like structure appears in the ideal long-range interaction case. The extracted excitation and correlation propagation velocities in the ideal long-range interaction case are about one order of magnitude larger than those in the multi-power-law interaction case and about two orders of magnitude larger than those in the short-range interaction case. These results indicate that the waveguide-quantum electrodynamics system with long-range interaction can boost the quantum information transfer speed and is beneficial for building fast quantum network and scalable quantum computer.

Lieb-Robinson Light Cone for Power-Law Interactions

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/r^{α} 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 r^{min{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.

Lieb-Robinson Bound and Almost-Linear Light Cone in Interacting Boson Systems

In this work, we investigate how quickly local perturbations propagate in interacting boson systems with Bose-Hubbard-type Hamiltonians. In general, these systems have unbounded local energies, and arbitrarily fast information propagation may occur. We focus on a specific but experimentally natural situation in which the number of bosons at any one site in the unperturbed initial state is approximately limited. We rigorously prove the existence of an almost-linear information-propagation light cone, thus establishing a Lieb-Robinson bound: the wave front grows at most as t log^{2}(t). We prove the clustering theorem for gapped ground states and study the time complexity of classically simulating one-dimensional quench dynamics, a topic of great practical interest.