When do non-Gaussian bosonic operators define a quantum operation?

We address the issue of quantifying the non-Gaussian character of a bosonic quantum state and introduce a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state. We analyze in detail the properties of the proposed measure and exploit it to evaluate the non-Gaussianity of some relevant single-mode and multimode quantum states. The evolution of non-Gaussianity is also analyzed for quantum states undergoing the processes of Gaussification by loss and de-Gaussification by photon-subtraction. The suggested measure is easily computable for any state of a bosonic system and allows one to define a corresponding measure for the non-Gaussian character of a quantum operation.We address the issue of quantifying the non-Gaussian character of a bosonic quantum state and introduce a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state. We analyze in detail the properties of the proposed measure and exploit it to evaluate the non-Gaussianity of some relevant single-mode and multimode quantum states. The evolution of non-Gaussianity is also analyzed for quantum states undergoing the processes of Gaussification by loss and de-Gaussification by photon-subtraction. The suggested measure is easily computable for any state of a bosonic system and allows one to define a corresponding measure for the non-Gaussian character of a quantum operation.

arXiv:0704.0639Physical Review AOct 22, 2007169 citations

Non-Gaussian Entanglement Hierarchy Based on the Schmidt Number

Jiajie Guo, Shuheng Liu, Matteo Fadel +1 more

Non-Gaussian entanglement is a promising resource in various quantum tasks. A recently defined class identifies entanglement that cannot be generated by applying Gaussian operations to separable inputs. To further explore the entanglement in this context, we introduce a quantitative witness $E_{\rm NG}$ in bipartite bosonic systems, which satisfies $E_{\rm NG}=1$ for all Gaussian-entanglable states, while $E_{\rm NG}>1$ certifies non-Gaussian entanglement. Its ceiling $d=\lceil E_{\rm NG}\rceil$ provides a lower bound on the Schmidt number irreducible by Gaussian transformations, thereby defining a natural hierarchy of non-Gaussian entanglement. For pure states, the condition is sharp and the hierarchy reflects the complexity of state learning. We benchmark the framework with some paradigmatic non-Gaussian states, such as NOON states and squeezed Kerr states, and analyze its robustness against loss. Moreover, we construct an experimentally economical NOON-type witness requiring only four density-matrix element measurements. These results establish an operationally meaningful and experimentally accessible framework for identifying non-Gaussian entanglement resources in continuous-variable quantum platforms.Non-Gaussian entanglement is a promising resource in various quantum tasks. A recently defined class identifies entanglement that cannot be generated by applying Gaussian operations to separable inputs. To further explore the entanglement in this context, we introduce a quantitative witness $E_{\rm NG}$ in bipartite bosonic systems, which satisfies $E_{\rm NG}=1$ for all Gaussian-entanglable states, while $E_{\rm NG}>1$ certifies non-Gaussian entanglement. Its ceiling $d=\lceil E_{\rm NG}\rceil$ provides a lower bound on the Schmidt number irreducible by Gaussian transformations, thereby defining a natural hierarchy of non-Gaussian entanglement. For pure states, the condition is sharp and the hierarchy reflects the complexity of state learning. We benchmark the framework with some paradigmatic non-Gaussian states, such as NOON states and squeezed Kerr states, and analyze its robustness against loss. Moreover, we construct an experimentally economical NOON-type witness requiring only four density-matrix element measurements. These results establish an operationally meaningful and experimentally accessible framework for identifying non-Gaussian entanglement resources in continuous-variable quantum platforms.

quant-pharXiv:2605.18605May 19, 20260 citations

Non-Hermitian Operators in Quantum Physics

Hynek Bíla

May 11, 20099 citations

On quantum operations as quantum states

Pablo J. Arrighi, Christophe Patricot

arXiv:quant-ph/0307024Annals of PhysicsDec 22, 200351 citations

Precision bounds for bosonic quantum batteries

Beatriz Polo, Federico Centrone

We study precision charging in bosonic quantum batteries under a finite-energy constraint, using the signal-to-noise ratio (SNR) of delivered excitations as an operational metric directly tied to the energy measured at a load. At the state level, we derive a classical bound whose violation is equivalent to antibunching and certifies non-classicality, and a Gaussian bound whose violation certifies non-Gaussianity under fixed temperature and energy-input constraints. We identify experimentally accessible non-Gaussian families that surpass this Gaussian bound at finite temperature, thereby establishing non-Gaussianity as a resource for enhanced charging precision. Finally, we introduce a linear photodetection model which, under standard linear-response assumptions, propagates these bounds to the photocurrent level and enables both witnesses to be evaluated solely from electrical statistics. Together, these results provide a realistic route to demonstrating an operational quantum advantage-defined as surpassing classical and Gaussian precision bounds-in a thermodynamically motivated energy-conversion task, with plausible near-term applications to the precision charging of fragile nanoscopic loads.We study precision charging in bosonic quantum batteries under a finite-energy constraint, using the signal-to-noise ratio (SNR) of delivered excitations as an operational metric directly tied to the energy measured at a load. At the state level, we derive a classical bound whose violation is equivalent to antibunching and certifies non-classicality, and a Gaussian bound whose violation certifies non-Gaussianity under fixed temperature and energy-input constraints. We identify experimentally accessible non-Gaussian families that surpass this Gaussian bound at finite temperature, thereby establishing non-Gaussianity as a resource for enhanced charging precision. Finally, we introduce a linear photodetection model which, under standard linear-response assumptions, propagates these bounds to the photocurrent level and enables both witnesses to be evaluated solely from electrical statistics. Together, these results provide a realistic route to demonstrating an operational quantum advantage-defined as surpassing classical and Gaussian precision bounds-in a thermodynamically motivated energy-conversion task, with plausible near-term applications to the precision charging of fragile nanoscopic loads.

arXiv:2505.24604May 30, 20250 citations

E_{\rm NG}

in bipartite bosonic systems, which satisfies

E_{\rm NG}=1

for all Gaussian-entanglable states, while

E_{\rm NG}>1

certifies non-Gaussian entanglement. Its ceiling

d=\lceil E_{\rm NG}\rceil

provides a lower bound on the Schmidt number irreducible by Gaussian transformations, thereby defining a natural hierarchy of non-Gaussian entanglement. For pure states, the condition is sharp and the hierarchy reflects the complexity of state learning. We benchmark the framework with some paradigmatic non-Gaussian states, such as NOON states and squeezed Kerr states, and analyze its robustness against loss. Moreover, we construct an experimentally economical NOON-type witness requiring only four density-matrix element measurements. These results establish an operationally meaningful and experimentally accessible framework for identifying non-Gaussian entanglement resources in continuous-variable quantum platforms.