Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements
arXiv:2407.04673 · doi:10.1103/PRXQuantum.6.020317
Abstract
Measurement correlations in quantum systems can exhibit non-local behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, the explicit construction of local hidden-variable (LHV) models remains an outstanding challenge in the general setting. To address this, we develop an approach that employs gradient-descent algorithms from machine learning to find LHV models which reproduce the statistics of arbitrary measurements for quantum many-body states. In contrast to previous approaches, our method employs a general ansatz, enabling it to discover an LHV model in all cases where the state is local. Therefore, it provides actual estimates for the critical noise levels at which two-qubit Werner states and three-qubit GHZ and W states become non-local. Furthermore, we find evidence suggesting that two-spin subsystems in the ground states of translationally invariant Hamiltonians are local, while bigger subsystems are in general not. Our method now offers a quantitative tool for determining the regimes of non-locality in any given physical context, including scenarios involving non-equilibrium and decoherence.
6+12 pages, 4+5 figures, GitHub: https://github.com/Nick-von-Selzam/AutoLHVs
References in corpus (36)
- Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
- Bell nonlocality
- Violation of Bell's inequality under strict Einstein locality conditions
- Significant-loophole-free test of Bell's theorem with entangled photons
- A strong loophole-free test of local realism
- A high-bias, low-variance introduction to Machine Learning for physicists
- Matrix product states represent ground states faithfully
- Detection-Loophole-Free Test of Quantum Nonlocality, and Applications
- Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes
- Grothendieck's constant and local models for noisy entangled quantum states
- Classical randomness in quantum measurements
- Genuine quantum correlations in quantum many-body systems: a review of recent progress
- More efficient Bell inequalities for Werner states
- Noise robustness of the nonlocality of entangled quantum states
- Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant
- General method for constructing local-hidden-variable models for entangled quantum states
- Algorithmic construction of local hidden variable models for entangled quantum states
- Bell inequalities and entanglement at quantum phase transition in the XXZ Model
- Nonlocality and entanglement in the XY model
- Machine Learning Bell Nonlocality in Quantum Many-body Systems
- Machine learning non-local correlations
- Genuinely multipartite entangled quantum states with fully local hidden variable models and hidden multipartite nonlocality
- A neural network oracle for quantum nonlocality problems in networks
- Entangled qutrits violate local realism stronger than qubits - an analytical proof
- Entanglement and nonlocality are inequivalent for any number of particles
- Genuine three-partite entangled states with a local hidden variable model
- Qutrit witness from the Grothendieck constant of order four
- Towards Grothendieck Constants and LHV Models in Quantum Mechanics
- Bell correlations in a many-body system with finite statistics
- Entanglement and Nonlocality in Infinite 1D Systems
- Machine Learning and Quantum Devices
- Improved local models and new Bell inequalities via Frank-Wolfe algorithms
- Violation of Bell inequality in perfect translation invariant systems
- Numerically assisted determination of local models in network scenarios
- Violation of the Bell inequality in quantum critical random spin- chains
- General spin systems without genuinely multipartite nonlocality