2025/12/29 by Ole Steuernagel, Steuernagel, Ole, Ray‐Kuang Lee +1
Physics and Astronomy · Computer Science · #Quantum Mechanics and Applications #Quantum Information and Cryptography #Quantum Computing Algorithms and Architecture
paper · doi:10.48550/arxiv.2512.23299
If the phase space-based Glauber-Sudarshan distribution, Pρ, has negative values the quantum state,~ρ, it describes is nonclassical. Due to P's singular behaviour this simple criterion is impractical to use. Recent work [Bohmann and Agudelo, Phys. Rev. Lett. 124, 133601 (2020)] presented a general, sensitive, and noise-tolerant certification functional,~ξ[P], for the detection of non-classical behaviour of quantum states Pρ. There, it was shown that when this functional takes on negative values somewhere in phase space,~ξ[P](x,p) < 0, this is sufficient to certify the nonclassicality of a state. Here we give examples where this certification fails. We investigate states which are known to be nonclassical but the certification functions is non-negative, ξ(x,p) ≥ 0, everywhere in phase space. We generalize ξ giving it an appealing form which allows for improved certification. This way we generate a more sensitive family of certification functions. Yet, also these fail for very weakly nonclassical states, the question how to faithfully certify quantumness remains an open question.