Characterizing correlation within multipartite quantum systems via local randomized measurements
arXiv:2108.08045 · doi:10.1103/PhysRevA.105.022407
Abstract
Given a quantum system on many qubits split into a few different parties, how many total correlations are there between these parties? Such a quantity, aimed to measure the deviation of the global quantum state from an uncorrelated state with the same local statistics, plays an important role in understanding multipartite correlations within complex networks of quantum states. Yet, the experimental access of this quantity remains challenging as it tends to be non-linear, and hence often requires tomography which becomes quickly intractable as dimensions of relevant quantum systems scale. Here, we introduce a much more experimentally accessible quantifier of total correlations, which can be estimated using only single-qubit measurements. It requires far fewer measurements than state tomography and obviates the need to coherently interfere multiple copies of a given state. Thus, we provide a tool for proving multipartite correlations that can be applied to near-term quantum devices.
arXiv comment28 pages, 8 figures. Comments are welcome
References in corpus (68)
- Quantum entanglement
- Quantum Computing in the NISQ era and beyond
- Variational Quantum Algorithms
- Entanglement detection
- The classical-quantum boundary for correlations: discord and related measures
- Measuring entanglement entropy through the interference of quantum many-body twins
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Quantum thermalization through entanglement in an isolated many-body system
- The role of quantum information in thermodynamics --- a topical review
- Unified View of Quantum and Classical Correlations
- Exact and Approximate Unitary 2-Designs: Constructions and Applications
- Probing entanglement entropy via randomized measurements
- Theory of variational quantum simulation
- GADZOOKS! Antineutrino Spectroscopy with Large Water Cerenkov Detectors
- Universal Quantum Estimator
- Direct estimations of linear and non-linear functionals of a quantum state
- Quantum-assisted quantum compiling
- Quantum Data Hiding
- Detecting Genuine Multipartite Entanglement with Two Local Measurements
- Entanglement Certification From Theory to Experiment
- Quantum certification and benchmarking
- Mixed-state entanglement from local randomized measurements
- Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
- Symmetry-resolved entanglement detection using partial transpose moments
- The structure of multidimensional entanglement in multipartite systems
- Efficient estimation of Pauli observables by derandomization
- Sample-optimal tomography of quantum states
- Quantum fidelity measures for mixed states
- Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
- Genuine quantum correlations in quantum many-body systems: a review of recent progress
- Cross-Platform Verification of Intermediate Scale Quantum Devices
- The power of random measurements: measuring Tr(ρ^n) on single copies of ρ
- Theory of quantum system certification: a tutorial
- Genuine quantum and classical correlations in multipartite systems
- Probing scrambling using statistical correlations between randomized measurements
- Single-copies estimation of entanglement negativity
- Measuring Multipartite Concurrence with a Single Factorizable Observable
- Many-body topological invariants from randomized measurements
- Entanglement detection beyond the cross-norm or realignment criterion
- Quantum Fisher information from randomized measurements
- Postulates for measures of genuine multipartite correlations
- Further results on entanglement detection and quantification from the correlation matrix criterion
- Total correlations of the diagonal ensemble herald the many-body localization transition
- Characterizing multipartite entanglement with moments of random correlations
- Experimental quantum state measurement with classical shadows
- Many-body Chern number from statistical correlations of randomized measurements
- The structure of Renyi entropic inequalities
- Experimental estimation of the quantum Fisher information from randomized measurements
- Entanglement negativity spectrum of random mixed states: A diagrammatic approach
- The Clifford group fails gracefully to be a unitary 4-design
- Mutual information-assisted Adaptive Variational Quantum Eigensolver
- Overlapped grouping measurement: A unified framework for measuring quantum states
- Experimental Optimal Verification of Entangled States using Local Measurements
- Quantum scrambling with classical shadows
- Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states
- Multipartite Entanglement Analysis From Random Correlations
- Detecting multipartite entanglement structure with minimal resources
- Correlations between outcomes of random measurements
- Quantifying genuine multipartite correlations and their pattern complexity
- Entanglement Structure: Entanglement Partitioning in Multipartite Systems and Its Experimental Detection Using Optimizable Witnesses
- Importance sampling of randomized measurements for probing entanglement
- Structural Quantification of Entanglement
- Entanglement characterization using quantum designs
- Experimental detection of entanglement with optimal-witness families
- Statistically significant tests of multiparticle quantum correlations based on randomized measurements
- Minimal tomography with entanglement witnesses
- Entanglement detection under coherent noise: Greenberger-Horne-Zeilinger-like states
- Characterizing coherence with quantum observables
Cited by in corpus (13)
- Entanglement barrier and its symmetry resolution: theory and experiment
- Detecting entanglement in quantum many-body systems via permutation moments
- Performance analysis of multi-shot shadow estimation
- Entanglement detection with trace polynomials
- Efficient Characterizations of Multiphoton States with an Ultra-thin Optical Device
- Collective randomized measurements in quantum information processing
- Quantum separability criteria based on realignment moments
- Quantifying multiparticle entanglement with randomized measurements
- Robust ultra-shallow shadows
- Local measurement strategies for multipartite entanglement quantification
- Generating quantum dissonance via local operations
- Detecting high-dimensional entanglement by randomized product projections
- Investigating the effect of noise channels on the quality of unitary t-designs