Entanglement Monogamy via Multivariate Trace Inequalities

Communications in Mathematical Physics, vol. 405

Abstract

Abstract Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative entropies based on restricted measurements of multipartite quantum systems. By combining these with multivariate matrix trace inequalities, we recover and sometimes strengthen various existing entanglement monogamy inequalities. In particular, we give direct, matrix-analysis-based proofs for the faithfulness of squashed entanglement by relating it to the relative entropy of entanglement measured with one-way local operations and classical communication, as well as for the faithfulness of conditional entanglement of mutual information by relating it to the separably measured relative entropy of entanglement. We discuss variations of these results using the relative entropy to states with positive partial transpose, and multipartite setups. Our results simplify and generalize previous derivations in the literature that employed operational arguments about the asymptotic achievability of information-theoretic tasks.

Authors 2

1. Mario Berta corresponding Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University, Aachen, Germany

2. Marco Tomamichel

   National University of Singapore · Centre for Quantum Technologies

   Affiliation as printed

   Centre for Quantum Technologies, National University of Singapore, Singapore, Singapore

   Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore