Observable estimation of entanglement of formation and quantum discord for bipartite mixed quantum states

TL;DR

This paper introduces experimentally accessible bounds for entanglement of formation and quantum discord in bipartite mixed states, enabling estimation from minimal measurements on two copies of the state.

Contribution

It provides a practical method to estimate EOF and QD bounds using only a few measurements on twofold copies of unknown bipartite states.

Findings

Derived observable bounds for EOF and QD.

Applied bounds to real experimental data.

Demonstrated feasibility of bounds with minimal measurements.

Abstract

We present observable lower and upper bounds for the entanglement of formation (EOF) and quantum discord (QD), which facilitates estimates of EOF and QD for arbitrary experimental unknown states in finite-dimensional bipartite systems. These bounds can be easily obtained by a few experimental measurements on a twofold copy $\varrho\otimes\varrho$ of the mixed states. Based on our results, we use the experimental measurement data of the real experiment given by Schmid \textit{et al.} [Phys. Rev. Lett. \textbf{101}, 260505 (2008)] to obtain the lower and upper bounds of EOF and QD for the experimental unknown state.