Variational quantum algorithm for entanglement quantification

Quantum entanglement is a foundational resource in quantum information science, underpinning applications across physics. However, detecting and quantifying entanglement remains a significant challenge. In this article, we introduce a variational quantum algorithm inspired by Uhlmann's theorem to quantify the Bures entanglement of general quantum states, a method that naturally extends to other quantum resources, including genuine multipartite entanglement, quantum discord, quantum coherence, and total correlations, while also enabling reconstruction of the closest free states. The algorithm requires a polynomial number of ancillary qubits and circuit depth relative to the system size, dimensionality, and free-state cardinality, making it scalable for practical implementations. Thus, it provides a versatile framework for quantifying quantum resources, demonstrated here through several applications.