Measuring entanglement without local addressing in quantum many-body simulators via spiral quantum state tomography

Abstract: Quantum state tomography serves as a key tool for identifying quantum states generated in quantum computers and simulators, typically involving local operations on individual particles or qubits to enable independent measurements. However, this approach requires an exponentially larger number of measurement setups as quantum platforms grow in size, highlighting the necessity of more scalable methods to efficiently perform quantum state estimation. Here, we present a tomography scheme that scales far more efficiently and, remarkably, eliminates the need for local addressing of single constituents before measurements. Inspired by the ``spin-spiral'' structure in magnetic materials, our scheme combines a series of measurement setups, each with different spiraling patterns, with compressed sensing techniques. The results of the numerical simulations demonstrate a high degree of tomographic efficiency and accuracy. Additionally, we show how this method is suitable for the measurement of specific entanglement properties of interesting quantum many-body states, such as entanglement entropy, under various realistic experimental conditions. This method offers a positive outlook across a wide range of quantum platforms, including those in which precise individual operations are challenging, such as optical lattice systems.