Towards a Faithful Quantumness Certification Functional for One-Dimensional Continuous-Variable Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912938111008768 |
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| author | Steuernagel, Ole Lee, Ray-Kuang |
| author_facet | Steuernagel, Ole Lee, Ray-Kuang |
| contents | If the phase space-based Glauber-Sudarshan distribution, $P_ρ$, 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 $P_ρ$. There, it was shown
that when this functional takes on negative values somewhere in phase space,~$ξ[P](x,p) < 0$, this is
\emph{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, $ξ(x,p) \geq 0$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23299 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards a Faithful Quantumness Certification Functional for One-Dimensional Continuous-Variable Systems Steuernagel, Ole Lee, Ray-Kuang Quantum Physics If the phase space-based Glauber-Sudarshan distribution, $P_ρ$, 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 $P_ρ$. There, it was shown that when this functional takes on negative values somewhere in phase space,~$ξ[P](x,p) < 0$, this is \emph{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, $ξ(x,p) \geq 0$, 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. |
| title | Towards a Faithful Quantumness Certification Functional for One-Dimensional Continuous-Variable Systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.23299 |