New additivity properties of the relative entropy of entanglement  - Roberto Rubboli | TQC 2023
Channel: Squid: Schools for Quantum Information Development
Date: 2023-08-24

Roberto Rubboli 
New additivity properties of the relative entropy of entanglement and its generalizations 

https://arxiv.org/abs/2211.12804
We prove that the relative entropy of entanglement is additive when at least one of the two states belongs to some specific class. We show that these classes include bipartite pure, maximally correlated, GHZ, Bell diagonal, isotropic, and generalized Dicke states. Previously, additivity was established only if both states belong to the same class. Moreover, we extend these results to entanglement monotones based on the $\alpha$-$z$ Rényi relative entropy. Notably, this family of monotones includes also the generalized robustness of entanglement and the geometric measure of entanglement. In addition, we prove that any monotone based on a quantum relative entropy is not additive for general states. 
We also compute closed-form expressions of the monotones for bipartite pure, Bell diagonal, isotropic, generalized Werner, generalized Dicke, and maximally correlated Bell diagonal states. Our results rely on proving new necessary and sufficient conditions for the optimizer of the monotones based on the $\alpha$-$z$ R'enyi relative entropy, which allow us to reduce the original optimization problem to a simpler linear one.
Even though we focus mostly on entanglement theory, we formulate some of our technical results in a general resource theory framework, and we expect that they could be used to investigate other resource theories.

July 27, 2023
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TQC 2023 | 24-28 July 2023, University of Aveiro, Portugal
http://tqc-conference.org

18th Conference on the  Theory of Quantum Computation, Communication and Cryptography.

TQC is a leading annual international conference for students and researchers working in the theoretical aspects of quantum information science. The scientific objective is to bring together the theoretical quantum information science community to present and discuss the latest advances in the field.


Organisation:
Squids - Schools for Quantum Information Development  
Universidade de Aveiro: Departamento de Matemática, CIDMA & Fábrica


Sponsors:
Phasecraft, UK
Google Quantum AI, USA
QuSoft, The Netherlands
Quantum for Life Centre, Denmark
Technology Innovation Institute, UAE
ML4Q, Germany
Dulwich Quantum