Inductive Bipartite Entanglement Detection using Spin Squeezing

Quantum entanglement is an essential asset in the areas of quantum computing and quantum communication. The practical detection of entanglement presents challenges, for instance, entanglement metrics, such as entanglement negativity, are hard to measure in realistic mixed systems of many degrees of freedom. In this study, we propose an inductive measurement protocol that effectively sidesteps the complexities of a full state tomography. Our protocol relies on the intrinsic quantum property that the local entanglement allowed within one subsystem is constrained by its entanglement with the other subsystem. We demonstrate that, in a lowly-mixed multi-qubit system such constraints can be identified by optimizing local spin squeezing within one subsystem, and they serve as a good indicator of the bipartite entanglement between both subsystems. One of the advantages of this protocol is that it relies only on local measurements of a single subsystem, such as spin-squeezing, which are readily available in most experimental setups. Finally, we illustrate how this protocol can be generalized to heterogeneous spin-boson systems for the characterization of complex entangled states.