Probing Topological Entanglement on Large Scales

Area of Science:

• Quantum Physics
• Condensed Matter Physics
• Quantum Information Science

Background:

• Topologically ordered quantum matter displays complex long-range entanglement patterns.
• Subsystem entropies are key indicators of topological order but are challenging to measure in large systems.

Purpose of the Study:

• To develop a practical protocol for measuring long-range topological entanglement.
• To enable the certification of topological order through subsystem entropy measurements on smaller scales.

Main Methods:

• A protocol employing local adiabatic deformations of the Hamiltonian.
• Extracting universal entanglement features from measurements on small, finite-sized subsystems.
• Trading an exponential number of measurements for polynomial-time quantum evolution.

Main Results:

• The proposed protocol successfully extracts universal features of long-range topological entanglement.
• Demonstrated applicability to various string-net models, including Abelian and non-Abelian phases.
• Numerical simulations confirmed the protocol's effectiveness in neutral atom tweezer arrays.

Conclusions:

• The protocol offers a feasible method for measuring topological entanglement in quantum systems.
• It significantly simplifies the experimental requirements for certifying topological order.
• The approach is general and adaptable to diverse quantum simulation platforms.