Superposition-state generation of nonorthogonal wavelike and particlelike states without ancillary qubits

The aim of this article is to generate the superposition state of nonorthogonal wavelike and particlelike states without ancillary qubits. Although it has been demonstrated that wavelike and particlelike states can be nonorthogonal, it remains unclear whether a superposition state of the two states can be achieved without the use of orthogonal ancillary qubits. To address this question, we employ a designed double-layer Mach-Zehnder interferometer that could continuously morph the single-photon state from particlelike to wavelike. Through both a theoretical analysis and experimental demonstration, we show that the nonorthogonality of wavelike and particlelike states can be maintained without ancillary qubits. The results showed that the two states are naturally nonorthogonal and can be directly utilized. As a variant of the delayed-choice experiment, our research will contribute to a deeper understanding of the nature of quantum objects, and also provide a different framework for discussions on wave-particle duality.