Extreme points of absolutely PPT states with exactly three distinct eigenvalues

• URL: http://arxiv.org/abs/2603.20717v1
• Date: Sat, 21 Mar 2026 08:52:03 GMT
• Title: Extreme points of absolutely PPT states with exactly three distinct eigenvalues
• Abstract summary: We show that every boundary point is an extreme point, with exactly one exception.<n>Most points become the known extreme points of exactly two distinct eigenvalues.
• Score: 6.083497020259863
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Whether the sets of absolutely separable (AS) and absolutely two-qutrit positive-partial-transpose (AP) states are the same has been an open problem in entanglement theory for decades. Since they are both convex sets, we investigate the boundary and extreme points of full-rank two-qutrit AP states with exactly three distinct eigenvalues. We show that every boundary point is an extreme point, with exactly one exception. We explicitly characterize the expressions of such points, each of which turns out to contain at most one parameter in some intervals. When the parameter approaches the ends of intervals, most points become the known extreme points of exactly two distinct eigenvalues. We present our results by tables and figures.

Related papers

• Frame-Dependent Traces and the Third-Particle Paradox [45.88028371034407]
  We show that the Paradox of the Third Particle arises when comparing subsystem descriptions across Quantum Reference Tracing perspectives.<n>We argue that our condition captures the Paradox content: rather than imposing consistency on the whole state space, we reproduce exactly the states on which it holds.
  arXiv  Detail & Related papers  (2026-07-23T18:00:01Z)
• Deterministic Zeroth-Order Mirror Descent via Vector Fields with A Posteriori Certification [45.85698554568285]
  We develop a deterministic zeroth-order mirror descent framework by replacing gradients with a general vector field.<n>Our analysis provides an evaluation template for last-rate inequality evaluations.<n>Together, these results expose a hidden geometric linking Bregman identities, deterministic certification, and robust conic geometry in zeroth-order mirror descent.
  arXiv  Detail & Related papers  (2026-01-31T10:05:05Z)
• Simple Relative Deviation Bounds for Covariance and Gram Matrices [34.99810116340191]
  We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings.<n>Our results provide sharper control across the spectrum.
  arXiv  Detail & Related papers  (2024-10-08T07:28:56Z)
• Separable ellipsoids around multipartite states [0.0]
  We show that around any $m$-partite product state $rho_rm prod=rho1-otimes...otimesrho_m$, there exists an ellipsoid of separable states centered around $_rm prod$.<n>This separable ellipsoid contains the separable ball proposed in previous works, and the volume of the ellipsoid is typically exponentially larger than that of the ball.<n>We further generalize this ellipsoidal criterion to a trace formula that yields separable region around all separable states, and
  arXiv  Detail & Related papers  (2024-10-07T18:05:26Z)
• On the extreme points of sets of absolulely separable and PPT states [6.9607365816307]
  The absolutely separable (resp. PPT) states remain separable (resp. positive partial transpose) under any global unitary operation. We show that each extreme point has at most three distinct eigenvalues. We also demonstrate that any extreme point in qutrit-qudit system has at most seven distinct eigenvalues.
  arXiv  Detail & Related papers  (2024-09-22T07:17:25Z)
• Maximally entangled real states and SLOCC invariants: the 3-qutrit case [0.0]
  We study the case of real 3-qutrit systems and discover a new set of maximally entangled states. It is notable that the Aharonov state is a simultaneous maximizer for all 3 fundamental invariants. We show how to evaluate these invariants on any 3-qutrit state using basic matrix operations.
  arXiv  Detail & Related papers  (2023-07-03T12:41:30Z)
• Almost Everything About the Unitary Almost Mathieu Operator [0.0]
  We show that supercritical, critical, and subcritical behavior all occur in this model. We also characterize the spectral type for each value of the coupling constant, almost every frequency, and almost every phase.
  arXiv  Detail & Related papers  (2021-12-06T18:17:31Z)
• H\"older Bounds for Sensitivity Analysis in Causal Reasoning [66.00472443147781]
  We derive a set of bounds on the confounding bias |E[Y|T=t]-E[Y|do(T=t)]| based on the degree of unmeasured confounding. These bounds are tight either when U is independent of T or when U is independent of Y given T.
  arXiv  Detail & Related papers  (2021-07-09T20:26:36Z)
• Eigenvalues of two-phase quantum walks with one defect in one dimension [0.30458514384586394]
  We study space-inhomogeneous quantum walks (QWs) on the integer lattice. We call them two-phase QWs with one defect. In this paper, we obtain a necessary and sufficient condition for the existence of eigenvalues.
  arXiv  Detail & Related papers  (2020-10-16T11:32:33Z)
• Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps [91.3755431537592]
  We show that any positive product of a qubit map with itself is decomposable. We characterize the cone of decomposable ququart Pauli diagonal maps.
  arXiv  Detail & Related papers  (2020-06-25T16:39:32Z)
• Infinite Feature Selection: A Graph-based Feature Filtering Approach [78.63188057505012]
  We propose a filtering feature selection framework that considers subsets of features as paths in a graph. Going to infinite allows to constrain the computational complexity of the selection process. We show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori.
  arXiv  Detail & Related papers  (2020-06-15T07:20:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.