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

Linear Algebra and its Applications

Partial traces and entropy inequalities

Rajendra Bhatia

Published Mar 25, 2003• 21 citations
Publisher
DOI
10.1016/s0024-3795(03)00386-0

Related papers

Inequalities related to partial transpose and partial trace

Daeshik Choi

Linear Algebra and its Applications•Nov 23, 2016•10 citations

Inequalities about partial transpose and partial traces

Daeshik Choi

We present inequalities related to partial transpose and partial traces of a positive semidefinite matrix.

Linear and Multilinear Algebra•Aug 18, 2017•8 citations

Entropy inequalities

Huzihiro Araki, Élliott H. Lieb

Communications in Mathematical Physics•Jun 1, 1970•568 citations

A UNIFIED TREATMENT OF CONVEXITY OF RELATIVE ENTROPY AND RELATED TRACE FUNCTIONS, WITH CONDITIONS FOR EQUALITY

Anna Jenčová, Mary Beth Ruskai

We consider a generalization of relative entropy derived from the Wigner–Yanase–Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint convexity of relative entropy, and for Tr K* ApK B1-pLieb's joint concavity in (A, B) for 0 < p < 1 and Ando's joint convexity for 1 < p ≤ 2. This approach allows us to obtain conditions for equality in these cases, as well as conditions for equality in a number of inequalities which follow from them. These include the monotonicity under partial traces, and some Minkowski type matrix inequalities proved by Carlen and Lieb for [Formula: see text]. In all cases, the equality conditions are independent of p; for extensions to three spaces they are identical to the conditions for equality in the strong subadditivity of relative entropy.

arXiv:0903.2895•Reviews in Mathematical Physics•Oct 1, 2010•61 citations

Entropy Inequalities

Huzihiro Araki, Élliott H. Lieb

Springer eBooks•Jan 1, 2002•12 citations

New partial trace inequalities and distillability of Werner states

Pablo Costa Rico

Abstract One of the oldest problems in quantum information theory is to study if there exists a state with negative partial transpose which is undistillable [1]. This problem has been open for almost 30 years, and still no one has been able to give a complete answer to it. This work presents a new strategy to try to solve this problem by translating the distillability condition on the family of Werner states into a problem of partial trace inequalities, this is the aim of our first main result. As a consequence, we obtain a new bound for the 2-distillability of Werner states, which does not depend on the dimension of the system. On the other hand, our second main result provides new partial trace inequalities for bipartite systems, connecting some of them also with the separability of Werner states. Throughout this work, we also present numerous partial trace inequalities, which are valid for many families of matrices.

arXiv:2310.05726•Letters in Mathematical Physics•May 4, 2025•3 citations
We consider a generalization of relative entropy derived from the Wigner–Yanase–Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint convexity of relative entropy, and for Tr K* ApK B1-pLieb's joint concavity in (A, B) for 0 < p < 1 and Ando's joint convexity for 1 < p ≤ 2. This approach allows us to obtain conditions for equality in these cases, as well as conditions for equality in a number of inequalities which follow from them. These include the monotonicity under partial traces, and some Minkowski type matrix inequalities proved by Carlen and Lieb for [Formula: see text]. In all cases, the equality conditions are independent of p; for extensions to three spaces they are identical to the conditions for equality in the strong subadditivity of relative entropy.
Abstract One of the oldest problems in quantum information theory is to study if there exists a state with negative partial transpose which is undistillable [1]. This problem has been open for almost 30 years, and still no one has been able to give a complete answer to it. This work presents a new strategy to try to solve this problem by translating the distillability condition on the family of Werner states into a problem of partial trace inequalities, this is the aim of our first main result. As a consequence, we obtain a new bound for the 2-distillability of Werner states, which does not depend on the dimension of the system. On the other hand, our second main result provides new partial trace inequalities for bipartite systems, connecting some of them also with the separability of Werner states. Throughout this work, we also present numerous partial trace inequalities, which are valid for many families of matrices.