arXiv subjects

Vu The Khoi

Publications and source records attributed to Vu The Khoi.

4 recordsLinked to original sources

arXiv2025

On the maximum purity of absolutely separable bipartite states

In this study, we investigate the problem of determining the maximum purity for absolutely separable and absolutely PPT quantum states. From the geometric viewpoint, this problem is equivalent to asking for the exact Euclidean radius of the smallest ball around the maximally mixed state that encompasses the set of all absolutely separable or absolutely PPT states. Our results provide an analytic solution for two qubit states. Based on numerical computation, we propose a conjectured maximum purity for absolutely separable qubit-qudit states and absolutely PPT qutrit-qudit states.

math-ph↗

arXiv2020

Left orderable surgeries of double twist knots II

A slope $r$ is called a left orderable slope of a knot $K \subset S^3$ if the 3-manifold obtained by $r$-surgery along $K$ has left orderable fundamental group. Consider two-bridge knots $C(2m, \pm 2n)$ and $C(2m+1, -2n)$ in the Conway notation, where $m \ge 1$ and $n \ge 2$ are integers. By using \textit{continuous} families of hyperbolic $\mathrm{SL}_2(\mathbb{R})$-representations of knot groups, it was shown in \cite{HT-genus1, Tr} that any slope in $(-4n, 4m)$ (resp. $[0, \max\{4m, 4n\})$) is a left orderable slope of $C(2m, 2n)$ (resp. $C(2m, - 2n)$) and in \cite{Ga} that any slope in $(-4n,0]$ is a left orderable slope of $C(2m+1,-2n)$. However, the proofs of these results are incomplete since the \textit{continuity} of the families of representations was not proved. In this paper, we complete these proofs and moreover we show that any slope in $(-4n, 4m)$ is a left orderable slope of $C(2m+1,-2n)$ detected by hyperbolic $\mathrm{SL}_2(\mathbb{R})$-representations of the knot group.

math.GT↗

arXiv2008

On the SU(2,1) representation space of the Brieskorn homology spheres

In this paper, we give a parameterization of the SU(2,1) representation space of the Brieskorn homology spheres using the trace coordinates. As applications, we give an example which shows that the orbifold Toledo invariant in \cite{krebs} does not distinguish the connected components of the PU(2,1) representation space.

math.GT↗

arXiv2005

On the symplectic volume of the moduli space of Spherical and Euclidean polygons

In this paper, we study the symplectic volume of the moduli space of polygons by using Witten's formula. We propose to use this volume as a measure for the flexibility of a polygon with fixed side-lengths. The main result of our is that among all the Spherical and Euclidean polygons with fixed perimeter the regular one is the most flexible and that among all the spherical polygons the regular one with side-length $π/2$ is the most flexible.

math.SG↗