Unveiling quantum entanglement in many-body systems from partial information

Abstract

Quantum entanglement is commonly assumed to be a central resource for quantum computing and quantum simulation. Nonetheless, the capability to detect it in many-body systems is severely limited by the absence of sufficiently scalable and flexible certification tools. This issue is particularly critical in situations where the structure of entanglement is a priori unknown, and where one cannot rely on existing entanglement witnesses. Here, we implement a scheme in which the knowledge of the mean value of arbitrary observables can be used to probe multipartite entanglement in a scalable, certified and systematic manner. Specifically, we rely on positive semidefinite conditions, independent of partial-transposition-based criteria, necessarily obeyed if the data can be reproduced by a separable state. The violation of any of these conditions yields a specific entanglement witness, tailored to the data of interest, revealing the salient features of the data which are impossible to reproduce without entanglement. We validate this approach by probing theoretical many-body states of several hundreds of qubits relevant to existing experiments: a single-particle quench in a one-dimensional $XX$ chain; a many-body quench in a two-dimensional $XX$ model with $1/r^3$ interactions; and thermal equilibrium states of Heisenberg and transverse-field Ising chains. In all cases, these investigations have lead us to discover new entanglement witnesses, some of which could be characterized analytically, generalizing existing results in the literature. In summary, our paper introduces a flexible data-driven entanglement detection technique for uncharacterized quantum many-body states, of immediate relevance to experiments in a quantum advantage regime.

published version

References in corpus (17)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Entanglement detection
• Quantum computational advantage using photons
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• 14-qubit entanglement: creation and coherence
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
• Spin squeezing and entanglement
• Choreographed entangle dances: topological states of quantum matter
• Detecting multipartite entanglement
• Multipartite entanglement detection via structure factors
• Experimental realisation of multipartite entanglement via quantum Fisher information in a uniform antiferromagnetic quantum spin chain
• Multiparticle covariance matrices and the impossibility of detecting graph state entanglement with two-particle correlations
• A family of multipartite separability criteria based on correlation tensor
• Quantum control of spin-correlations in ultracold lattice gases
• Relaxation of the collective magnetization of a dense 3D array of interacting dipolar S=3 atoms
• Detecting two-site spin-entanglement in many-body systems with local particle-number fluctuations

Cited by in corpus (16)

• Semidefinite programming relaxations for quantum correlations
• Probing quantum correlations in many-body systems: a review of scalable methods
• Semi-definite programming and quantum information
• Lower Bounding Ground-State Energies of Local Hamiltonians Through the Renormalization Group
• Dimension-free entanglement detection in multipartite Werner states
• Entanglement detection with trace polynomials
• Magnetic excitations, non-classicality and quantum wake spin dynamics in the Hubbard chain
• Entanglement transitivity problems
• Semi-device-independently characterizing quantum temporal correlations
• Introduction to quantum entanglement in many-body systems
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Quantifying High-Order Interdependencies in Entangled Quantum States
• Positive maps from the walled Brauer algebra
• State-witness contraction
• Entanglement and distillation from symmetric positive maps
• Universal entanglement entropy in the ground state of biased bipartite systems