A non-Hermitian loop for quantum measurement

Classical quantum simulators—including photonic lattices, electrical circuits, and metamaterials—have successfully emulated Schrödinger-type quantum evolution but lack a robust method to simulate quantum measurements. This prevents exploring measurement-enriched phases and post-measurement dynamics.

Here, we present a non-Hermitian framework enabling classical emulation of quantum state collapse through experimentally accessible parameter control [1]. Our protocol requires the system's Hamiltonian to execute a closed loop in parameter space during the measurement interaction, returning to its initial Hermitian form afterward.

For two-level systems, we exploit chiral state conversion around exceptional points: encircling an EP with clockwise versus anticlockwise parameter trajectories deterministically selects between eigenstates, effectively destroying superpositions. The loop chirality acts as a controllable measurement setting. Remarkably, this dynamics naturally privileges the initial Hamiltonian's eigenstates as stable outcomes.

This approach is directly implementable in existing platforms where non-Hermitian terms (gain/loss) and parameter modulation are routine. We discuss practical implementations, opening pathways to simulate measurement-based protocols in classical testbeds [1,2].

[1] L.E.F. Foa Torres & S. Roche, J. Phys. Commun. 9, 065001 (2025)

[2] For related references see https://www.foatorres.com/publications/