We notice that non-linear oscillator Hamiltonian having the character of non-Hermitian $(H \ne H^{+})$ , non-PT Symmetry $([H,PT] \ne 0)$ and non-Pseudohermiticity $(\eta H \eta^{-1}\ne H^{+})$ can yield real eigenvalues.We notice that non-linear oscillator Hamiltonian having the character of non-Hermitian $(H \ne H^{+})$, non-PT Symmetry $([H,PT] \ne 0)$ and non-Pseudohermiticity $(\eta H \eta^{-1}\ne H^{+})$ can yield real eigenvalues.

arXiv:1502.01004Feb 1, 20150 citations

Energetics of non-Gaussianity in single mode cavities

Sahil S. Jafar, Kian Hwee Lim, Kiarn T. Laverick +3 more

Non-Gaussian states are key resources for quantum technologies, making the quantification of non-Gaussianity a fundamental challenge. We introduce an energetic framework for characterizing non-Gaussianity in single-mode bosonic states by decomposing the total energy into Gaussian and non-Gaussian contributions. For pure states, we show that the non-Gaussian energy defines a bona fide measure of non-Gaussianity and establish a direct connection with the relative entropy of non- Gaussianity. As an illustration, we consider non-Gaussian states generated from coherent states with tunable amplitudes using a SNAP gate. We find that the resulting non-Gaussian energy and Wigner negativity are maximized at similar input amplitudes. For mixed states, we demonstrate that the non-Gaussian energy provides a faithful witness of non-Gaussianity. Our results uncover an energetic fine structure of non-Gaussian quantum states and offer new insights into the efficient generation and manipulation of non-Gaussian resources.Non-Gaussian states are key resources for quantum technologies, making the quantification of non-Gaussianity a fundamental challenge. We introduce an energetic framework for characterizing non-Gaussianity in single-mode bosonic states by decomposing the total energy into Gaussian and non-Gaussian contributions. For pure states, we show that the non-Gaussian energy defines a bona fide measure of non-Gaussianity and establish a direct connection with the relative entropy of non- Gaussianity. As an illustration, we consider non-Gaussian states generated from coherent states with tunable amplitudes using a SNAP gate. We find that the resulting non-Gaussian energy and Wigner negativity are maximized at similar input amplitudes. For mixed states, we demonstrate that the non-Gaussian energy provides a faithful witness of non-Gaussianity. Our results uncover an energetic fine structure of non-Gaussian quantum states and offer new insights into the efficient generation and manipulation of non-Gaussian resources.

quant-pharXiv:2606.31150Jul 1, 20260 citations

Anderson’s Orthogonality Theorem

Kei Yosida

Springer series in solid-state sciencesJan 1, 19960 citations

Foundations of Non-linear Quantum Mechanics

E. Rówiński

The foundations of non-linear quantum mechanics are based on six postulates and five propositions. On a first quantised level, these approaches are built on non-linear differential operators, non-linear eigenvalue equations, and the notion of non-linear observables and non-linear states. The present theory predicts that the non-linear function solution of a non-linear partial differential equation for a free particle is correct and that the commutator of the position operator and the non-linear momentum operator does not commute. Moreover, the implicit wave function of linear quantum mechanics can be determined by a non-linear wave function solution of non-linear partial differential equation, which also verifies the non-linear quantum mechanics.The foundations of non-linear quantum mechanics are based on six postulates and five propositions. On a first quantised level, these approaches are built on non-linear differential operators, non-linear eigenvalue equations, and the notion of non-linear observables and non-linear states. The present theory predicts that the non-linear function solution of a non-linear partial differential equation for a free particle is correct and that the commutator of the position operator and the non-linear momentum operator does not commute. Moreover, the implicit wave function of linear quantum mechanics can be determined by a non-linear wave function solution of non-linear partial differential equation, which also verifies the non-linear quantum mechanics.

arXiv:1901.05088Jan 15, 20190 citations

Unitarity

Martinus J. G. Veltman

Cambridge University Press eBooksJun 16, 19940 citations

We notice that non-linear oscillator Hamiltonian having the character of non-Hermitian

(H \ne H^{+})

, non-PT Symmetry

([H,PT] \ne 0)

and non-Pseudohermiticity

(\eta H \eta^{-1}\ne H^{+})

can yield real eigenvalues.