Monogamy-of-entanglement-inspired protocol to quantify bipartite entanglement using spin squeezing

TL;DR

This paper introduces a monogamy-of-entanglement-inspired protocol that uses spin squeezing to detect and quantify bipartite entanglement in multi-qubit systems, offering an alternative to full state tomography.

Contribution

It proposes a novel protocol leveraging spin squeezing and monogamy of entanglement to efficiently detect and quantify bipartite entanglement without full state tomography.

Findings

Analytical results for small systems, especially GHZ states.

Improved accuracy with optimal squeezing Hamiltonian for larger systems.

Protocol applicable where state tomography is difficult.

Abstract

Quantum entanglement is an essential resource for quantum science and technology. However, entanglement detection and quantification, via typical entanglement measures such as linear entanglement entropy or negativity, can be a very challenging task. Here we propose a protocol to detect bipartite entanglement in a system of $N$ qubits inspired by the concept of monogamy of entanglement, where, given a total system in a pure state with some bipartite entanglement between two subsystems, subsequent unitary evolution and measurement of one of the subsystems may be used to quantify the entanglement between the two. To address the difficulty of detection, we propose to use spin squeezing to quantify the entanglement within the individual subsystem. Knowing that the relation between spin squeezing and some entanglement measures is not one-to-one, we give some suggestions on how a judicious choice of squeezing Hamiltonian can lead to better results in our protocol. For systems with a small number of qubits, we derive analytical results and show how our protocol can work optimally for GHZ states. For larger systems, we show how the accuracy of the protocol can be improved by a proper choice of the squeezing Hamiltonian. Our protocol presents an alternative for entanglement detection in platforms where state tomography is inaccessible or hard to perform. Additionally, the ideas presented here can be extended beyond spin-only systems to expand their applicability.