Quantum Systems, Codes, and Information
Q.4.7
Lecture
Quantum Information Theory

Quantification of Unextendible Entanglement and Its Applications in Entanglement Distillation

Xin Wang, Mark Wilde, Kun Wang

Date & Time

01:00 am – 01:00 am

Abstract

The unextendibility or monogamy of entangled states is a key property of quantum entanglement. Unlike conventional ways of expressing entanglement monogamy via entanglement measure inequalities, we develop a state-dependent resource theory to quantify the unextendibility of bipartite entangled states. First, we introduce a family of entanglement measures called \textit{unextendible entanglement}. Given a bipartite state $\rho_{AB}$, the key idea behind these measures is to minimize a divergence between $\rho_{AB}$ and any possibly reduced state $\rho_{AB'}$ of an extension $\rho_{ABB'}$ of $\rho_{AB}$. These measures are intuitively motivated by the fact that the more a bipartite state is entangled, the less each of its individual systems can be entangled with a third party. Second, we show that the unextendible entanglement is an entanglement monotone under two-extendible operations, which include local operations and one-way classical communication as a special case. Unextendible entanglement has several other desirable properties, including normalization and faithfulness. As applications, we show that the unextendible entanglement provides efficiently computable benchmarks for the rate of perfect entanglement distillation, as well as for the overhead of entanglement distillation.


Presenters

Mark Wilde

Louisiana State University

Kun Wang

Southern University of Science and Technology

Session Chair

Marco Tomamichel

National University of Singapore