Qubit-parity interference despite unknown interaction phases

Abstract Quantum interference between interacting systems is fundamental to basic science and quantum technology, but it typically requires precise control of the interaction phases of lasers or microwave generators. Can interference be observed if those interaction phases are stable but unknown, usually prohibitive for complex state without active control? Here, we answer this question by experimentally preparing a Schrödinger-cat-like state of an internal qubit and a motional oscillator of a trapped 40 Ca + ion, and its robustness to such uncontrolled phases. By applying alternating red and blue sideband pulses, we enforce a strict qubit-parity correlation and interference inherently insensitive to stable but unknown phases of the driving laser. For this qubit-parity interference, we use a minimal two-pulse interferometric sequence to demonstrate characteristic visibilities of 20% and 40%, which approach the theoretical visibility limit, providing a scalable coherence witness without full state tomography for high-dimensional states, demonstrated here for motional superpositions with mean phonon number $\langle \hat{n}\rangle \approx 4.1$ 〈 n ˆ 〉 ≈ 4.1 and standard deviation $\Delta \hat{n} \approx 2.9$ Δ n ˆ ≈ 2.9 .