This study presents a method to measure entanglement entropy in a system of interacting particles using quantum interference of many-body twins. The researchers used a quantum gas microscope to prepare and interfere two identical copies of a four-site Bose-Hubbard system. This many-body interference enabled them to measure quantities not directly accessible in a single system, such as quadratic functions of the density matrix. These measurements allowed them to determine the quantum purity, Rényi entanglement entropy, and mutual information of the system. Entanglement is a fundamental feature of quantum mechanics, describing non-local correlations between quantum objects. It plays a crucial role in quantum information sciences and has broad implications in various fields, including condensed matter physics and quantum gravity. The study demonstrates how entanglement can be measured in systems of interacting delocalized particles, which is challenging due to the lack of direct experimental methods. The researchers used the principle of quantum superposition and the concept of partial measurements to detect entanglement. By ignoring information about one subsystem, they could determine if the other subsystem became a classical mixture of pure quantum states. This was quantified by measuring the quantum purity, defined as the trace of the density matrix squared. For a pure quantum state, the quantum purity is 1, while for a mixed state, it is less than 1. The study also showed that entanglement can be measured using the second-order Rényi entropy, which is related to the quantum purity. The Rényi entropy provides a lower bound for the von Neumann entanglement entropy and is gaining importance in theoretical condensed matter physics. The researchers demonstrated that entanglement can be detected in the ground state of the Bose-Hubbard model, showing how the system transitions from a Mott insulator to a superfluid phase. The study also explored non-equilibrium entanglement dynamics, showing how entanglement can grow in time in infinite systems, leading to interesting many-body physics such as thermalization in closed quantum systems. The results highlight the importance of entanglement in understanding quantum phases and dynamics of strongly-correlated many-body systems. The method presented can be extended to fermionic systems and systems with internal degrees of freedom, offering a powerful tool for measuring entanglement in various quantum systems.This study presents a method to measure entanglement entropy in a system of interacting particles using quantum interference of many-body twins. The researchers used a quantum gas microscope to prepare and interfere two identical copies of a four-site Bose-Hubbard system. This many-body interference enabled them to measure quantities not directly accessible in a single system, such as quadratic functions of the density matrix. These measurements allowed them to determine the quantum purity, Rényi entanglement entropy, and mutual information of the system. Entanglement is a fundamental feature of quantum mechanics, describing non-local correlations between quantum objects. It plays a crucial role in quantum information sciences and has broad implications in various fields, including condensed matter physics and quantum gravity. The study demonstrates how entanglement can be measured in systems of interacting delocalized particles, which is challenging due to the lack of direct experimental methods. The researchers used the principle of quantum superposition and the concept of partial measurements to detect entanglement. By ignoring information about one subsystem, they could determine if the other subsystem became a classical mixture of pure quantum states. This was quantified by measuring the quantum purity, defined as the trace of the density matrix squared. For a pure quantum state, the quantum purity is 1, while for a mixed state, it is less than 1. The study also showed that entanglement can be measured using the second-order Rényi entropy, which is related to the quantum purity. The Rényi entropy provides a lower bound for the von Neumann entanglement entropy and is gaining importance in theoretical condensed matter physics. The researchers demonstrated that entanglement can be detected in the ground state of the Bose-Hubbard model, showing how the system transitions from a Mott insulator to a superfluid phase. The study also explored non-equilibrium entanglement dynamics, showing how entanglement can grow in time in infinite systems, leading to interesting many-body physics such as thermalization in closed quantum systems. The results highlight the importance of entanglement in understanding quantum phases and dynamics of strongly-correlated many-body systems. The method presented can be extended to fermionic systems and systems with internal degrees of freedom, offering a powerful tool for measuring entanglement in various quantum systems.