7 citations · 8 across the 15 of their papers we have counts for
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Positive Planar Measures for Spectral Pinching and the Corrected BMV Conjecture
Trung Hoa Dinh, Cong Trinh Le, Trung Dung Vuong
We prove the corrected Bessis--Moussa--Villani pinching conjecture for all symmetrized word averages. For Hermitian matrices and , we construct a positive compactly…
Weighted Two-Parameter Quantum Divergences Generated by Matrix Power-Mean Gaps
Trung Hoa Dinh, Minh Toan Ho, Ha Trang Nguyen +1
Let be the cone of complex positive definite matrices. For and , let denote the weighted matrix power mean, with the logarithm…
Determinantal Kernel Schemes of Matrix Nets and Applications to Positive Maps
Trung Hoa Dinh, Minh Toan Ho, Cong Trinh Le +1
For a linear map on a matrix space, we study the projective schemes obtained by intersecting its projectivized kernel with determinantal rank loci. For matrix nets, that is, three…
Demailly's Conjecture in Quantum Language and Its Solution
Trung Hoa Dinh
We give an exact translation between fat-point interpolation in complex projective space and a dark-state problem for fixed-particle-number bosons. Under the unitary Fischer--Bargm…
Frobenius dilation of Hilbert function, Demailly's conjecture, and varieties of powers
Trung Hoa Dinh, Tai Huy Ha
We prove a Frobenius-dilation inequality for Hilbert functions of ideals generated by powers of fixed homogeneous forms in characteristic zero. Via Emsalem--Iarrobino inverse syste…
Heron-Wasserstein majorization inequalities for spectral and Kubo-Ando geometric means
Trung Dung Vuong, Anh Thi Nguyen, Trung Hoa Dinh
We prove sharp Heron-type majorization inequalities for two quadratic matrix expressions associated with the spectral and Kubo-Ando geometric means. For the spectral geometric mean…
On the Failure of the Upper Bound in the Refined BMV Conjecture and a Pinching Correction
Trung Hoa Dinh
We analyze why the refined Bessis--Moussa--Villani conjecture fails. The refined conjecture proposed that the normalized trace average over all words with prescribed numbers of let…
Spectral geometric mean and trace characterizations
Airat Bikchentaev, Trung Hoa Dinh, Anh Vu Le +1
We use nearly parallel pure states to characterize positive linear functionals on as positive multiples of the trace if and only if $ϕ(A \natural B) \leq \sqrt{ϕ…
A Weighted Spectral Quantum Fidelity
Cong Trinh Le, The Khoi Vu, Minh Toan Ho +1
We introduce and study a one-parameter family of fidelity-type quantities based on the weighted spectral geometric mean, which we call the \emph{weighted spectral fidelity} \( \mat…