Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements

• URL: http://arxiv.org/abs/2407.04673v1
• Date: Fri, 5 Jul 2024 17:31:35 GMT
• Title: Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements
• Authors: Nick von Selzam, Florian Marquardt,
• Abstract summary: Measurement correlations in quantum systems can exhibit non-local behavior. We develop an approach that employs gradient-descent algorithms from machine learning to find LHV models. Our method now offers a quantitative tool for determining the regimes of non-locality in any given physical context.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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