Many-body Chern number from statistical correlations of randomized measurements

Understand

One of the main topological invariants that characterizes several topologically-ordered phases is the many-body Chern number (MBCN).

• Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in different atomic and photonic quantum platforms in the near future.
• Experimental measurement and numerical computation of this invariant is conventionally based on the linear-response techniques which require having access to a family of states, as a function of an external parameter, which is not suitable for many quantum simulators.
• Here, we propose an ancilla-free experimental scheme for the measurement of this invariant, without requiring any knowledge of the Hamiltonian.