Related papers: Every PPT channel has finite entanglement breaking index

Every PPT channel has finite entanglement breaking index

URL: http://arxiv.org/abs/2608.13551v2
Date: Mon, 17 Aug 2026 17:48:51 GMT
Title: Every PPT channel has finite entanglement breaking index
Abstract summary: We prove that every PPT linear map has finite entanglement breaking index.<n>We also show that a large family of PPT maps, which strictly contains the class of 2-superpositive maps, has entanglement breaking index bounded above by 3.
Score: 6.52489063705362
License: http://creativecommons.org/publicdomain/zero/1.0/
Abstract: We prove that every PPT linear map has finite entanglement breaking index, thereby establishing the eventual entanglement breaking property of PPT channels in full generality. Furthermore, by utilizing completely positive maps with low entanglement dimensionality, we show that a large family of PPT maps, which strictly contains the class of 2-superpositive maps, has entanglement breaking index bounded above by 3, uniformly in the dimension. In particular, these results provide evidence that the PPT-cubed conjecture may hold in full generality.

Related papers

Beyond the Positive Partial Transpose Squared Conjecture: The Qutrit Case [0.42970700836450476]
Entanglement swapping is a fundamental operation in quantum repeaters for establishing entanglement between distant parties.<n>We show that the cone of $1$-undistillable CP maps is exactly the largest qutrit cone of CP maps.<n>Although map composition captures only the standard maximally entangled outcome in entanglement swapping, we prove that any $1$-undistillable two-qutrit state and any state of Schmidt number at most two cannot generate terminal entanglement.
arXiv Detail & Related papers (2026-07-17T13:32:14Z)
Sparse anisotropic positive maps for qutrit entanglement: exact indecomposability and PPT geometry [0.0]
We introduce and analyze an exactly solvable family of sparse bistochastic positive maps on qutrits.<n>We show that positivity holds exactly on the square $0le w,zle2/3$, complete positivity on the smaller square $0le w,zle2/3$, and decomposability is lost precisely outside a quarter circle in the corner.<n>Although $W_*$ is not optimal, we give an explicit optimal refinement whose detection region on this family is strictly larger.
arXiv Detail & Related papers (2026-07-14T07:55:02Z)
Dimension Reduction for Curves: Simplified and Generalized [56.23281156053955]
We revisit random projections for reducing the dimension of high-dimensional polygonal curves.<n>We give a simplified proof of the known $O(varepsilon-2log(nm))$ bound on the target dimension of a random projection.<n>Our proof is based on the concept of sparse oblivious subspace embeddings.
arXiv Detail & Related papers (2026-07-03T08:48:35Z)
Detecting bipartite entanglement with PnCP maps and non-negative polynomials [0.7036032466145112]
We show how to generate PnCP maps based on the construction of certain positive non-Sum-of-Squares.<n>We numerically investigate their entanglement power, demonstrating notably that they are capable of detecting entangled states.
arXiv Detail & Related papers (2026-05-28T18:00:06Z)
Cartan-covariant Quantum Channels and the PPT$^{2}$ conjecture [0.0]
We show that Cartan-covariant channels have a covariance Lie group that forms a Cartan decomposition of SU$(D)$.<n>The regions of completely positive and completely co-positive Cartan-covariant trace-preserving maps are found through a spectral analysis of the Choi state.
arXiv Detail & Related papers (2025-01-07T17:46:43Z)
Degradable Strongly Entanglement Breaking Maps [0.0]
We prove that unital degradable entanglement breaking maps are precisely the $C*$-extreme points of the convex set of unital entanglement breaking maps on matrix algebras.
arXiv Detail & Related papers (2023-04-01T13:14:27Z)
Annihilating Entanglement Between Cones [77.34726150561087]
We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
arXiv Detail & Related papers (2021-10-22T15:02:39Z)
ME-PCN: Point Completion Conditioned on Mask Emptiness [50.414383063838336]
Main-stream methods predict missing shapes by decoding a global feature learned from the input point cloud. We present ME-PCN, a point completion network that leverages emptiness' in 3D shape space.
arXiv Detail & Related papers (2021-08-18T15:02:27Z)
PMP-Net: Point Cloud Completion by Learning Multi-step Point Moving Paths [54.459879603473034]
We design a novel neural network, named PMP-Net, to mimic the behavior of an earth mover. It moves each point of the incomplete input to complete the point cloud, where the total distance of point moving paths should be shortest. It learns a strict and unique correspondence on point-level, which can capture the detailed topology and structure relationships between the incomplete shape and the complete target.
arXiv Detail & Related papers (2020-12-07T01:34:38Z)
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)
SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS [55.41644538483948]
Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projectedangled Pair States (PEPS) Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder. Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence.
arXiv Detail & Related papers (2019-12-31T16:30:25Z)

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