Observing super-quantum correlations across the exceptional point in a single, two-level trapped ion

Quantum theory provides rules governing much of the microscopic world, and among its counter-intuitive consequences are correlations that exceed the bounds from local, classical theories. In qubits, unitary dynamics theoretically limit these spatiotemporal quantum correlations, called Bell/Clauser-Horn-Shimony-Holt or Leggett-Garg inequalities, to 2sqrt(2) or 1.5 respectively. Experiments with state-of-the-art qubits have approached these bounds. Here, using a dissipative, trapped ⁴⁰Ca⁺ ion governed by a two-level, non-Hermitian Hamiltonian, we observe temporal correlation values up to 1.768(8) for the Leggett-Garg parameter K₃, exceeding the Lüder's bound of 1.5. Distinct evolution speeds for antipodal qubit states, which violate the unified bound for the transit time based on quantum speed limit, result in the super-quantum K₃ values observed over a wide parameter range. Our results demonstrate that post-selected, coherent dynamics of non-Hermitian Hamiltonians pave the way for enhanced quantum correlations that exceed protocols based on unitary or dissipative dynamics.