Entanglement of Local Hidden States

Matteo Fadel1,2 and Manuel Gessner3,4

1Department of Physics, ETH Zürich, 8093 Zürich, Switzerland
2Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
3ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels (Barcelona), Spain
4Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005, Paris, France

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Steering criteria are conditions whose violation excludes the possibility of describing the observed measurement statistics with local hidden state (LHS) models. When the available data do not allow to exclude arbitrary LHS models, it may still be possible to exclude LHS models with a specific separability structure. Here, we derive experimentally feasible criteria that put quantitative bounds on the multipartite entanglement of LHS. Our results reveal that separable states may contain hidden entanglement that can be unlocked by measurements on another system, even if no steering between the two systems is possible.

The Einstein-Podolsky-Rosen paradox is a counterintuitive phenomenon enabled by a particular form of quantum correlations, known as steering. An observation of this paradox implies that no quantum state assigned locally to a system, together with classical correlations, is able to explain the observed measurement results. In many cases, excluding all possible local quantum states is extremely challenging due to demanding requirements on experimental noise. We show that even if the data cannot reveal steering, it may still be possible to exclude certain classes of local quantum states, in particular those that are separable. Our work introduces families of experimentally testable criteria that reveal correlations that can only be reproduced with entangled local states. Moreover, the entanglement that is hidden in these states can be unlocked by remote measurements and classical communication.

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[2] Kuan-Yi Lee, Jhen-Dong Lin, Adam Miranowicz, Franco Nori, Huan-Yu Ku, and Yueh-Nan Chen, "Steering-enhanced quantum metrology using superpositions of noisy phase shifts", Physical Review Research 5 1, 013103 (2023).

[3] Jiajie Guo, Feng-Xiao Sun, Daoquan Zhu, Manuel Gessner, Qiongyi He, and Matteo Fadel, "Detecting Einstein-Podolsky-Rosen steering in non-Gaussian spin states from conditional spin-squeezing parameters", Physical Review A 108 1, 012435 (2023).

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