Abstract: 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., npj Quantum Information 11, 152 (2025) https://arxiv.org/abs/2411.03132

[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