Hermitian Sums
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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)...
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...
An Algebraic-Diagrammatic Construction for Vertex Corrections to the $GW$ Self-Energy
new Abstract: The $G3W2$ approximation -- the second-order self-energy beyond $GW$ -- is known to violate some fundamental analytic properties of the self-energy. In particular, its lack of positive semi-definiteness leads to unphysical features such as negative spectral functions. In this work, we reformulate the $G3W2$ approximation within the algebraic-diagrammatic construction (ADC) framework.