Entanglement concentration via measurement:- role of imaginarity

TL;DR

This paper explores how complex-valued measurements, rooted in the resource theory of imaginarity, enhance entanglement concentration and swapping protocols, leading to improved quantum network percolation efficiency.

Contribution

It demonstrates the operational advantage of complex measurement bases in entanglement protocols and constructs new bases that outperform standard ones, addressing open problems.

Findings

Complex measurements significantly improve bipartite entanglement concentration.

A new three-qubit basis surpasses the GHZ basis in entanglement generation.

Application reduces bond occupation probability and entanglement requirements in quantum networks.

Abstract

The role of complex numbers in quantum theory extends beyond mathematical convenience, having recently been formalized as a resource under the framework of the resource theory of imaginarity. Operationally, imaginarity translates into using fewer resources in optical setups. In this work, we investigate the operational advantage offered by complex-valued measurements in the entanglement of assistance protocol for three-qubit systems. We demonstrate that employing such measurement bases leads to a significant improvement in the concentration of bipartite entanglement with the aid of the third party. We further analyze a modified entanglement swapping protocol and show that a three-qubit complex measurement bases with certain symmetries outperform the standard GHZ-basis. This is also one example where a three-qubit non-maximally entangled basis surpasses a maximally entangled one in generating entanglement. Construction of the basis also addresses the open problems raised in [Phys. Rev. A. \textbf{108}, 022220 (2023)]. As an intriguing application, we show that using this approach in quantum network percolation on a honeycomb lattice reduces the required bond occupation probability by $22.7\%$ and, requirement of entanglement by $10.6\%$ in each bond.