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arXiv:2311.06094 · Quantum

Certification of quantum state functions under partial information

Leonardo Zambrano, Donato Farina, Egle Pagliaro, Márcio M. Taddei, Antonio Acín

Published Aug 16, 2024• 6 citations
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Abstract

Convex functions of quantum states play a key role in quantum physics, with examples ranging from Bell inequalities to von Neumann entropy. However, in experimental scenarios, direct measurements of these functions are often impractical. We address this issue by introducing two methods for determining rigorous confidence bounds for convex functions based on informationally incomplete measurements. Our approach outperforms existing protocols by providing tighter bounds for a fixed confidence level and number of measurements. We evaluate the performance of our methods using both numerical and experimental data. Our findings demonstrate the efficacy of our approach, paving the way for improved quantum state certification in real-world applications.

DOI
10.22331/q-2024-08-16-1442

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The activation of Bell nonlocality is a protocol that enables the violation of a Bell inequality from a system that initially did not allow for any such violation because the state of the system was Bell-local. This activation of hidden Bell nonlocality has been demonstrated in experiments; however, while the certification of Bell nonlocality is conceptional straightforward, a statistically rigorous verification that the initial state is Bell-local has not yet been achieved. This is due to two key obstacles: The lack of a method to establish a suitable confidence region from the measured data and the need for an efficient technique to verify Bell locality of all states within the confidence region. In this work, we address both challenges. We introduce a confidence polytope in the form of a hyperoctahedron and provide a computationally efficient method to verify whether a quantum state admits a local hidden state model, thus being unsteerable and, consequently, Bell-local. Using these methods, we find that a statistically rigorous certification of hidden Bell nonlocality needs of the order of 109{10}^{9}109 samples.