Symmetric extendibility of quantum states

TL;DR

This paper investigates the properties of symmetric extendibility in quantum states, its implications for quantum security, and introduces a new monotone to analyze one-way security and distillability in quantum systems.

Contribution

It introduces a new one-way monotone based on symmetric approximation and explores the link between symmetric extendibility, distillability, and security in quantum states.

Findings

Symmetric extendibility impacts quantum security and distillability.

A new monotone based on symmetric approximation is proposed.

Geometric analysis reveals structures with significant symmetric extendible components.

Abstract

Studies on symmetric extendibility of quantum states become especially important in a context of analysis of one-way quantum measures of entanglement, distilabillity and security of quantum protocols. In this paper we analyse composite systems containing a symmetric extendible part with a particular attention devoted to one-way security of such systems. Further, we introduce a new one-way monotone based on the best symmetric approximation of quantum state. We underpin those results with geometric observations on structures of multi-party settings which posses in sub-spaces substantial symmetric extendible components. Finally, we state a very important conjecture linking symmetric-extendibility with one-way distillability and security of all quantum states analyzing behavior of private key in neighborhood of symmetric extendible states.