7 citations · 8 across the 15 of their papers we have counts for
18 papers
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…
Quantum Algorithms for Computing Maximal Quantum -divergence and Kubo-Ando means
Trung Hoa Dinh, Nhat A. Nghiem
The development of quantum computation has resulted in many quantum algorithms for a wide array of tasks. Recently, there is a growing interest in using quantum computing technique…
A new estimation of the quantum Chernoff bound
Mohsen Kian, Trung Hoa Dinh, Mohammad Sal Moslehian +1
Relating to finding possible upper bounds for the probability of error for discriminating between two quantum states, it is well-known that \begin{align*} \mathrm{tr}(A+B) - \mathr…
Matrix power means and new characterizations of operator monotone functions
Trung Hoa Dinh, Cong Trinh Le, The Van Nguyen +1
For positive definite matrices and , the Kubo-Ando matrix power mean is defined as $$ P_μ(p, A, B) = A^{1/2}\left(\frac{1+(A^{-1/2}BA^{-1/2})^p}{2}\right )^{1/p} A^{1/2}\qua…
Functions preserving operator means
Trung Hoa Dinh, Hiroyuki Osaka, Shuhei Wada
Let be a non-trivial operator mean in the sense of Kubo and Ando, and let the set of normalized positive operator monotone functions on . In this paper, w…
Some Geometric Properties of Matrix Means with respect to Different Distance Function
Trung Hoa Dinh, Raluca Dumitru, Jose A. Franco
In this paper we study the monotonicity, in-betweenness and in-sphere properties of matrix means with respect to Bures-Wasserstein, Hellinger and Log-Determinant metrics. More prec…
Two trace inequalities for operator functions
Trung Hoa Dinh, Minh Toan Ho, Cong Trinh Le +1
In this paper we show that for a non-negative operator monotone function on such that and for any positive semidefinite matrices and , $$ Tr((A-B…
Some applications of Scherer-Hol's theorem for polynomial matrices
Trung Hoa Dinh, Minh Toan Ho, Cong Trinh Le
In this paper we establish some applications of the Scherer-Hol's theorem for polynomial matrices. Firstly, we give a representation for polynomial matrices positive definite on su…
On the Pólya-Szegö operator inequality
Trung Hoa Dinh, Hamid Reza Moradi, Mohammad Sababheh
In this paper, we present generalized Pólya-Szegö type inequalities for positive invertible operators on a Hilbert space for arbitrary operator means between the arithmetic and the…
New characterizations of operator monotone functions
Trung Hoa Dinh, Raluca Dumitru, Jose Franco
If is a symmetric mean and is an operator monotone function on , then Conversely, Ando and Hiai showed th…
Some inequalities for operator (p,h)-convex functions
Trung Hoa Dinh, Khue TB Vo
Let be a positive number and a function on satisfying for any . A non-negative continuous function on $K (\s…