Many-body entropies and entanglement from polynomially-many local measurements
arXiv:2311.08108 · doi:10.1103/PhysRevX.14.031035
Abstract
Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical post-processing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments, and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix which allow us to reconstruct entropies and PT moments from information on local subsystems. This yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements (RMs), providing a practical and common measurement scheme, we prove that our protocol only requires polynomially-many measurements and post-processing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators, and provide numerical evidence that they are satisfied in more general, physically-interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today's quantum platforms.
arXiv comment30 pages, 10 figures; v2: references added and general revision
References in corpus (104)
- Quantum entanglement
- Quantum Computing in the NISQ era and beyond
- A computable measure of entanglement
- Quantum Simulation
- Area laws for the entanglement entropy - a review
- Entanglement entropy and conformal field theory
- The logarithmic negativity: A full entanglement monotone that is not convex
- Superconducting Qubits: Current State of Play
- 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
- Quantum state tomography via compressed sensing
- The ITensor Software Library for Tensor Network Calculations
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Matrix product states represent ground states faithfully
- Semiconductor Spin Qubits
- Efficient quantum state tomography
- Decay of Loschmidt Echo Enhanced by Quantum Criticality
- Probing entanglement entropy via randomized measurements
- Quantum Simulators: Architectures and Opportunities
- Tools for quantum simulation with ultracold atoms in optical lattices
- Measuring entanglement growth in quench dynamics of bosons in an optical lattice
- The randomized measurement toolbox
- Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
- Quantum simulation and computing with Rydberg-interacting qubits
- Reconstructing quantum states with generative models
- Mixed-state entanglement from local randomized measurements
- A Sharp Fannes-type Inequality for the von Neumann Entropy
- Stabilizer Rényi entropy
- Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
- Measuring entanglement entropy of a generic many-body system with a quantum switch
- Efficient tomography of a quantum many-body system
- Quantum Computer Systems for Scientific Discovery
- Permutationally invariant quantum tomography
- Efficient estimation of Pauli observables by derandomization
- Shannon and entanglement entropies of one- and two-dimensional critical wave functions
- Measurement-induced entanglement and teleportation on a noisy quantum processor
- Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
- Cross-Platform Verification of Intermediate Scale Quantum Devices
- The power of random measurements: measuring Tr(ρ^n) on single copies of ρ
- The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
- Perfect Sampling with Unitary Tensor Networks
- Quantum computers as universal quantum simulators: state-of-art and perspectives
- Machine Learning Assisted Many-Body Entanglement Measurement
- A review of Quantum Cellular Automata
- Sample-efficient learning of quantum many-body systems
- Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
- Permutationally invariant state reconstruction
- Quantifying nonstabilizerness of matrix product states
- Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
- Scalable reconstruction of density matrices
- Stabilizer entropies and nonstabilizerness monotones
- Measuring the Renyi entropy of a two-site Fermi-Hubbard model on a trapped ion quantum computer
- Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity
- Measuring entanglement using quantum quenches
- Multipartite entanglement detection in bosons
- Single-copies estimation of entanglement negativity
- Learning to Measure: Adaptive Informationally Complete Generalized Measurements for Quantum Algorithms
- Preparation of matrix product states with log-depth quantum circuits
- Continuity bounds for entanglement
- Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
- Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
- Magic-state resource theory for the ground state of the transverse-field Ising model
- Rényi entropy of a line in two-dimensional Ising models
- Exploring Large-Scale Entanglement in Quantum Simulation
- Negative eigenvalues of partial transposition of arbitrary bipartite states
- Experimental single-setting quantum state tomography
- Efficient quantum state tomography with convolutional neural networks
- Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
- Experimental Comparison of Efficient Tomography Schemes for a Six-Qubit State
- Optimal Entanglement Certification from Moments of the Partial Transpose
- Shannon and Rényi mutual information in quantum critical spin chains
- Entanglement barrier and its symmetry resolution: theory and experiment
- Characterizing multipartite entanglement with moments of random correlations
- Universal behavior of the Shannon mutual information of critical quantum chains
- Measuring nonstabilizerness via multifractal flatness
- Participation spectroscopy and entanglement Hamiltonian of quantum spin models
- Noiseless Quantum Circuits for the Peres Separability Criterion
- Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
- A Scalable Maximum Likelihood Method for Quantum State Tomography
- Scalable and Flexible Classical Shadow Tomography with Tensor Networks
- Quantum Cellular Automata, Tensor Networks, and Area Laws
- Markov entropy decomposition: a variational dual for quantum belief propagation
- Multipartite Entanglement Analysis From Random Correlations
- Quantum Approximate Markov Chains are Thermal
- Operator relaxation and the optimal depth of classical shadows
- Cross-Platform Comparison of Arbitrary Quantum Computations
- Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits
- Classifying Quantum Phases With The Torus Trick
- Sub-Quantum Fisher Information
- Closed-form analytic expressions for shadow estimation with brickwork circuits
- Learning quantum many-body systems from a few copies
- Enhanced estimation of quantum properties with common randomized measurements
- Typical Correlation Length of Sequentially Generated Tensor Network States
- Classical shadows based on locally-entangled measurements
- Sharp Continuity Bounds for Entropy and Conditional Entropy
- Sample-efficient estimation of entanglement entropy through supervised learning
- Decay of quantum conditional mutual information for purely generated finitely correlated states
- Entanglement phase diagrams from partial transpose moments
- Entropy scaling law and the quantum marginal problem
- Petz recovery versus matrix reconstruction
- Matrix product states and the decay of quantum conditional mutual information
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