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    Monogamy-of-entanglement-inspired protocol for quantifying bipartite entanglement using spin squeezing

    Diego Fallas Padilla1,2,3,*, Mingjian Zhu3, and Han Pu3,†

    • 1JILA and Department of Physics, University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
    • 2Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
    • 3Department of Physics and Astronomy, and Smalley-Curl Institute, Rice University, Houston, Texas 77251-1892, USA

    • *Contact author: difa1788@colorado.edu
    • †Contact author: hpu@rice.edu

    Phys. Rev. A 111, 062419 – Published 13 June, 2025

    DOI: https://doi.org/10.1103/hvmh-h7h8

    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 Greenberger-Horne-Zeilinger (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.

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