Many-body entropies and entanglement from polynomially-many local measurements

Understand

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 post-processing 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 yields a simple and efficient strategy for entropy and entanglement estimation.