Hermitian
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Related Articles from SNS
QEC and EAQEC Codes from Hermitian Sums and Hulls of Cyclic Codes over $\mathbb{F}_2 \times (\mathbb{F}_2+v\mathbb{F}_2)$
new Abstract: In this work, we determine the generator polynomials for the Hermitian hulls and Hermitian sums of cyclic codes defined over the composite ring $\mathbb{F}_2 \times (\mathbb{F}_2 + v\mathbb{F}_2)$, where $v^2 = v$. Based on these structures, we develop quantum error-correcting (QEC) codes by applying the Hermitian dual version of Quantum Construction~X to the obtained Hermitian hulls and sums. Moreover, by employing matrix product code methods on linear complementary dual (LCD)...
Arbitrary-Order Scattering Exceptional Points in Configurable Non-Hermitian Zero-Index Materials
new Abstract: Scattering exceptional points (EPs) are non-Hermitian degeneracies where the eigenvalues and eigenvectors of scattering matrices coalesce, enabling many intriguing phenomena in optical systems. Higher-order scattering EPs are particularly notable for their ultrasensitive response to perturbations, yet achieving flexible, arbitrary-order control remains challenging. Here, we propose a configurable non-Hermitian zero-index material (ZIM) network that enables arbitrary-order...
An indefinite LOBPCG type of algorithm for detecting a definite Hermitian matrix pair
Announce Type: new Abstract: A Hermitian matrix pair $(A,B)$ is called definite if some real linear combination of the matrices $A$ and $B$ is a positive definite matrix. Detection of the definiteness is not straightforward. We propose a basic subspace algorithm for detecting a large definite matrix pair $(A,B)$ with indefinite $B$. The proposed subspace algorithm is based on iterative testing of small projected Hermitian matrix pairs formed by using subspaces of small dimensions.
Solving 2D Black Scholes Equation via Hermitian Block Embedding and Generalised Quantum Signal Processing
arXiv:2606.00458v1 Announce Type: cross Abstract: The Black Scholes equation provides a fundamental model for the no arbitrage pricing of financial derivatives. After finite difference discretisation, the pricing problem can be formulated as a finite dimensional linear algebra problem involving the inverse of a non Hermitian time step matrix. Recent advances in quantum linear algebra algorithms, particularly the generalised quantum signal processing (GQSP)algorithm, enable matrix functions...
Fundamental Limits of Non-Hermitian Sensing from Quantum Fisher Information
arXiv:2603.10614v2 Announce Type: replace-cross Abstract: Exceptional points (EPs) exhibit strongly enhanced spectral responses and are therefore promising candidates for sensing applications. Whether these non-Hermitian degeneracies provide a genuine advantage in the quantum regime has been the subject of ongoing debate.
Complex-gauge control of anomalous Floquet corner responses in a non-Hermitian physical-synthetic photonic lattice
arXiv:2606.07038v2 Announce Type: replace-cross Abstract: We propose a non-Hermitian Floquet photonic lattice formed by a physical resonator coordinate and a synthetic frequency coordinate. A two-step modulation protocol realizes a chiral walk in this physical-synthetic plane, with a real synthetic flux controlling loop interference and imaginary gauge fields controlling non-reciprocal envelopes. We show that anomalous corner pairs at quasienergies zero and \(\pi/T\) exhibit three distinct...
Complex-gauge control of anomalous Floquet corner responses in a non-Hermitian physical-synthetic photonic lattice
Announce Type: cross Abstract: We propose a non-Hermitian Floquet photonic lattice formed by a physical resonator coordinate and a synthetic frequency coordinate. A two-step modulation protocol realizes a chiral walk in this physical-synthetic plane, with a real synthetic flux controlling loop interference and imaginary gauge fields controlling non-reciprocal envelopes. We show that anomalous corner pairs at quasienergies zero and \(\pi/T\) exhibit three distinct layers of physics.
Transverse spin texture in optical non-Hermitian skin modes
arXiv:2606.02189v1 Announce Type: new Abstract: In structured electromagnetic fields, polarization textures are often closely linked to the spatial variation of the energy flow. However, this familiar picture has been established mainly for lossless and isotropic settings, and concrete examples showing how it is modified in media with gain and loss remain limited. Here, we demonstrate that optical skin modes associated with the non-Hermitian skin effect (NHSE) carry a finite transverse...
Normal forms of unidirectional coupling in quasi-phase-matched non-Hermitian systems
Announce Type: new Abstract: Optimal conditions for unidirectional coupling in quasi-phase-matched non-Hermitian systems are analyzed for both autonomous and externally driven configurations. The quasi-phase-matched coupling mechanism is due to periodic modulation of the real and imaginary parts of the coupling interface, which results in unequal coupling coefficients between interacting waves. The conventional parity-time (PT) symmetry theory suggests that the strongest unidirectionality...
Optimal Control and Dissipativity of Linear Hermitian Matrix-Valued Dynamical Systems
arXiv:2606.08856v1 Announce Type: cross Abstract: We develop a unified framework for linear-cost optimal control, finite-time optimal steering, dissipativity analysis, and zero-sum differential games for linear impulsive systems whose state is a Hermitian matrix evolving in $\mathbb{H}^{n+m}_{\succeq0}$, a class that encompasses continuous- and discrete-time linear systems and switched systems as degenerate cases, and includes the second-order moment dynamics of linear (stochastic) hybrid...