Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2112.13667

A note on positive partial transpose blocks

Mohammad Alakhrass

Published Dec 22, 2021• 0 citations
arXivHTMLPDF

Abstract

In this article, we study the class of PPT blocks. We introduce several inequalities, related to this class, with an emphasis on comparing the main diagonal and the off-diagonal components of a 2 by 2 PPT block.
DOI
10.48550/arxiv.2112.13667

Related papers

A note on positive partial transpose blocks

Moh. Alakhrass

In this article, we study the class of positive partial transpose blocks. We introduce several inequalities related to this class with an emphasis on comparing the main diagonal and off-diagonal components of a $ 2 \times 2 $ positive partial transpose block.

AIMS Mathematics•Jan 1, 2023•3 citations

On Positive Partial Transpose Matrices

Mehmet Gumus, Jianzhen Liu, Samir Raouafi +1 more

This paper mainly focuses on the class of $2 \times 2$ block PPT matrices. The relationship between PPT matrices and the norm inequalities is further explored. Some properties of a non-PPT matrix in terms of its eigenvalues are investigated. Moreover, a number of useful sufficient conditions for a matrix to be PPT are provided.

Electronic Journal of Linear Algebra•May 13, 2020•1 citation

Linear maps of positive partial transpose matrices and singular value inequalities

Xiaohui Fu, Pan-Shun Lau, Tin-Yau Tam

Linear maps : M n M k are called m -PPT if [(A i j )] m i, j=1 are positive partial transpose matrices for all positive semi-definite matrices

Mathematical Inequalities & Applications•Jan 1, 2020•2 citations

On positive and positive partial transpose matrices

İbrahim Halil Gümüş, Hamid Reza Moradi, Mohammad Sababheh

A block matrix $\left[ \begin{smallmatrix}A & X \\{{X}^{*}} & B \\\end{smallmatrix} \right]$ is positive partial transpose (PPT) if both $\left[ \begin{smallmatrix}A & X \\{{X}^{*}} & B \\\end{smallmatrix} \right]$ and $\left[ \begin{smallmatrix}A & {{X}^{*}} \\X & B \\\end{smallmatrix} \right]$ are positive semi-definite. This class is significant in studying the separability criterion for density matrices. The current paper presents new relations for such matrices. This includes some equivalent forms and new related inequalities that extend some results from the literature. In the end of the paper, we present some related results for positive semi-definite block matrices, which have similar forms as those presented for PPT matrices, with applications that include significant improvement of numerical radius inequalities.

Electronic Journal of Linear Algebra•Dec 15, 2022•6 citations

On a characterization of PPT states

W. A. Majewski

We present two different descriptions of positive partially transposed (PPT) states. One is based on the theory of positive maps while the second description provides a characterization of PPT states in terms of Hilbert space vectors. Our note is based on our previous results.

arXiv:0708.3980•Aug 29, 2007•3 citations

Partial trace inequalities for partial transpose of positive semidefinite block matrices

Junjian Yang, Huan Xu

Positivity•Mar 14, 2024•0 citations
This paper mainly focuses on the class of 2×22 \times 22×2 block PPT matrices. The relationship between PPT matrices and the norm inequalities is further explored. Some properties of a non-PPT matrix in terms of its eigenvalues are investigated. Moreover, a number of useful sufficient conditions for a matrix to be PPT are provided.
A block matrix [AXX∗B]\left[ \begin{smallmatrix}A & X \\{{X}^{*}} & B \\\end{smallmatrix} \right][AX∗​XB​] is positive partial transpose (PPT) if both [AXX∗B]\left[ \begin{smallmatrix}A & X \\{{X}^{*}} & B \\\end{smallmatrix} \right][AX∗​XB​] and [AX∗XB]\left[ \begin{smallmatrix}A & {{X}^{*}} \\X & B \\\end{smallmatrix} \right][AX​X∗B​] are positive semi-definite. This class is significant in studying the separability criterion for density matrices. The current paper presents new relations for such matrices. This includes some equivalent forms and new related inequalities that extend some results from the literature. In the end of the paper, we present some related results for positive semi-definite block matrices, which have similar forms as those presented for PPT matrices, with applications that include significant improvement of numerical radius inequalities.