article published yes Benoît Vermersch author Marko Ljubotina author F75EE9BE-5C90-11EA-905D-16643DDC885E0000-0003-0038-7068 J. Ignacio Cirac author Peter Zoller author Maksym Serbyn author 47809E7E-F248-11E8-B48F-1D18A9856A870000-0002-2399-5827 Lorenzo Piroli author MaSe department Non-Ergodic Quantum Matter: Universality, Dynamics and Control project Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical postprocessing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix, which allow us to reconstruct entropies and PT moments from information on local subsystems. This identification yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements providing a practical and common measurement scheme, we prove that our protocol requires only polynomially many measurements and postprocessing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators and provide numerical evidence that they are satisfied in more general, physically interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today’s quantum platforms. https://research-explorer.ista.ac.at/download/17493/17532/2024_PhysRevX_Vermersch.pdf application/pdfno American Physical Society2024 eng 2160-3308 2311.08108 00129966710000210.1103/physrevx.14.031035 143 B. Vermersch, M. Ljubotina, J.I. Cirac, P. Zoller, M. Serbyn, L. Piroli, Physical Review X 14 (2024). Vermersch, Benoît, et al. “Many-Body Entropies and Entanglement from Polynomially Many Local Measurements.” <i>Physical Review X</i>, vol. 14, no. 3, 031035, American Physical Society, 2024, doi:<a href="https://doi.org/10.1103/physrevx.14.031035">10.1103/physrevx.14.031035</a>. B. Vermersch, M. Ljubotina, J. I. Cirac, P. Zoller, M. Serbyn, and L. Piroli, “Many-body entropies and entanglement from polynomially many local measurements,” <i>Physical Review X</i>, vol. 14, no. 3. American Physical Society, 2024. Vermersch, B., Ljubotina, M., Cirac, J. I., Zoller, P., Serbyn, M., &#38; Piroli, L. (2024). Many-body entropies and entanglement from polynomially many local measurements. <i>Physical Review X</i>. American Physical Society. <a href="https://doi.org/10.1103/physrevx.14.031035">https://doi.org/10.1103/physrevx.14.031035</a> Vermersch B, Ljubotina M, Cirac JI, Zoller P, Serbyn M, Piroli L. 2024. Many-body entropies and entanglement from polynomially many local measurements. Physical Review X. 14(3), 031035. Vermersch B, Ljubotina M, Cirac JI, Zoller P, Serbyn M, Piroli L. Many-body entropies and entanglement from polynomially many local measurements. <i>Physical Review X</i>. 2024;14(3). doi:<a href="https://doi.org/10.1103/physrevx.14.031035">10.1103/physrevx.14.031035</a> Vermersch, Benoît, Marko Ljubotina, J. Ignacio Cirac, Peter Zoller, Maksym Serbyn, and Lorenzo Piroli. “Many-Body Entropies and Entanglement from Polynomially Many Local Measurements.” <i>Physical Review X</i>. American Physical Society, 2024. <a href="https://doi.org/10.1103/physrevx.14.031035">https://doi.org/10.1103/physrevx.14.031035</a>. 174932024-09-04T18:57:11Z2025-09-08T09:04:14Z