Estimation of the geometric measure of entanglement with Wehrl Moments through Artificial Neural Networks

Abstract

In recent years, artificial neural networks (ANNs) have become an increasingly popular tool for studying problems in quantum theory, and in particular entanglement theory. In this work, we analyse to what extent ANNs can accurately predict the geometric measure of entanglement of symmetric multiqubit states using only a limited number of Wehrl moments (moments of the Husimi function of the state) as input, which represents partial information about the state. We consider both pure and mixed quantum states. We compare the results we obtain by training ANNs with the informed use of convergence acceleration methods. We find that even some of the most powerful convergence acceleration algorithms do not compete with ANNs when given the same input data, provided that enough data is available to train these ANNs. We also provide an experimental protocol for measuring Wehrl moments, which is state-independent. More generally, this work opens up perspectives for the estimation of entanglement measures and other SU(2)-invariant quantities, such as the Wehrl entropy, in a way that is more accessible in experiments than by means of full state tomography.

arXiv comment27 pages, 14 figures v3: expanded manuscript with a new section on an experimental protocol for measuring Wehrl moments

References in corpus (39)

• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Many-body quantum state tomography with neural networks
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• The European Quantum Technologies Roadmap
• Reinforcement Learning with Neural Networks for Quantum Feedback
• Symmetry-resolved entanglement detection using partial transpose moments
• The geometric measure of entanglement for symmetric states
• Detection of multipartite entanglement in the vicinity of symmetric Dicke states
• Machine Learning Assisted Many-Body Entanglement Measurement
• When does reinforcement learning stand out in quantum control? A comparative study on state preparation
• Multiqubit symmetric states with high geometric entanglement
• The maximally entangled symmetric state in terms of the geometric measure
• Permutationally invariant state reconstruction
• Linking a distance measure of entanglement to its convex roof
• Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom
• Renyi-Wehrl entropies as measures of localization in phase space
• Prediction and real-time compensation of qubit decoherence via machine-learning
• Genuine multiparticle entanglement of permutationally invariant states
• Entanglement Classification via Neural Network Quantum States
• Proof of an entropy conjecture for Bloch coherent spin states and its generalizations
• Husimi distribution and phase space analysis of Dicke model quantum phase transition
• Second moment of the Husimi distribution as a measure of complexity of quantum states
• Continuous phase-space representations for finite-dimensional quantum states and their tomography
• Deep learning of quantum entanglement from incomplete measurements
• Moments of generalized Husimi distributions and complexity of many-body quantum states
• Tomographic reconstruction of the Wigner function on the Bloch sphere
• Quantum polarization tomography of bright squeezed light
• Neural networks for detecting multimode Wigner-negativity
• Matrix permanent and quantum entanglement of permutation invariant states
• Entropic entanglement criteria in phase space
• Exchange symmetry and global entanglement and full separability
• Mixed State Entanglement Classification using Artificial Neural Networks
• Inverted spectroscopy and interferometry for quantum-state reconstruction of systems with SU(2) symmetry
• Extracting many-particle entanglement entropy from observables using supervised machine learning
• Numerical and analytical results for geometric measure of coherence and geometric measure of entanglement
• Spin qudit tomography and state reconstruction error
• Wehrl entropy production rate across a dynamical quantum phase transition
• Tomography from collective measurements

Cited by in corpus (1)

• Efficient detection of nonclassicality using moments of the Wigner function