In this talk I shall review the work done in the past few years, inspired by a previously unnoticed observation by Tsirelson [1]: the Wigner negativity of some states of a single harmonic oscillator can be certified by measuring only one observable (say, position) at one among a set of suitable times. This is somewhat surprising, as it is common knowledge that the evolution of a harmonic oscillator is identical to the classical one in the Heisenberg representation. We improved the characterization of the original protocol for continuous variables and extended it to discrete variables [2,3], the latter case leading to the first experimental implementation [4]. We also modified the protocol to detect entanglement: for continuous variables, it gives an entanglement witness that is free of false positives [5]; for discrete variable, we reported the first witness that detects the GHZ state of N spins using only measurements of the total angular momentum [6,7]. On a more foundational level, the task being operational, it can be phrased in the language of generalized probabilistic theories: contrary to what happens for Bell inequalities, here quantum theory can always reach the maximal score [8] References: [1] B. Tsirelson, https://arxiv.org/abs/quant-ph/0611147 [2] L.H. Zaw et al., Phys. Rev. A 106, 032222 (2022) https://arxiv.org/abs/2204.10498 [3] L.H. Zaw, V.S., https://arxiv.org/abs/2411.03132, accepted in npj Quantum Information [4] A. Vartjees et al., Newton 1, 100017 (2025) https://arxiv.org/abs/2410.07641 [5] P. Jayachandran et al., Phys. Rev. Lett. 130, 160201 (2023) https://arxiv.org/abs/2210.10357 [6] K.-N. Huynh-Vu et al., Phys. Rev. A 109, 042402 (2024) https://arxiv.org/abs/2311.00806 [7] J. Chen et al., Phys. Rev. A 110, 062408 (2024) https://arxiv.org/abs/2410.07641 [8] L.H. Zaw et al. Phys. Rev. Lett. 134, 190201 (2025) https://arxiv.org/abs/2401.16147

Valerio Scarani is Professor at the Department of Physics and Principal Investigator at the Centre for Quantum Technologies (currently serving as deputy director) at the National University of Singapore. Over the years, his theoretical works has covered several areas, notably quantum cryptography and Bell nonlocality (a topic for which he has written a comprehensive treatise, Oxford University Press 2019), from foundations to collaborations with experimental groups.