Quantum Fisher information of the Klein--Gordon, $\phi^4$, and Dirac vacua

Abstract: The quantum Fisher information (QFI) of the vacuum of three quantum field theories is evaluated with respect to the mass parameter of each theory. All field theories are considered on a $(d+1)$-dimensional Euclidean spacetime. We consider the Klein-Gordon field, a quartic interaction ($\phi^4$) field theory, and the free Dirac field. In the case of the quartic interaction theory, the QFI is given perturbatively to first order in the interaction constant. For the free KG case, we find a $m^{d-2}$ dependence of the QFI, and thus no dependence for $d=2$, in agreement with the holographic duality characterizing the theory. The introduction of a quartic interaction is shown to lead to a QFI divergence in $d=3$ and to reduce the available information in the $d=0$ system. The vacuum QFI with respect to the free Dirac field mass is shown to be UV-divergent for $d=2$ and $d=3$, mass-dependent for $d=1$, and zero for $d=0$.

arXiv:2607.26919 [hep-th]

(or arXiv:2607.26919v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2607.26919 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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