Entanglement benchmarking in Quantum Simulations of Spin Systems.

Quantum phase transitions in many-body systems give rise to highly entangled states, and understanding these correlations is crucial for characterizing quantum materials. Traditional entanglement measures such as entanglement entropy are limited to pure states and require full state tomography, making them impractical for near-term quantum devices. Therefore, we explore the Positive Partial Transpose (PPT) criterion as an efficient and scalable entanglement witness in quantum spin models. It detects pairwise entanglement from reduced density matrices, distinguishes quantum from classical correlations, and applies to both pure and mixed states—making it ideal for studying condensed matter systems at finite temperatures. We prepare ground states of one-dimensional spin systems using matrix product states (MPS) and map them to quantum circuits via adiabatic evolution for efficient realization on quantum hardware. The PPT criterion captures clear signatures of phase transitions and is implemented on real hardware using Quantum Overlapping Tomography. This framework provides an efficient way to completely map the two-body entanglement structure in any state, including time-evolved and thermal states, on quantum computers.