Generalized monogamy of entanglement and quantification of bipartite entanglement*

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. We demonstrate that, given a total system 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 (for example, when only one subsystem is at disposal) or hard to perform. Additionally, the ideas presented here can be extended beyond spin-only systems to expand their applicability.