Entanglement-interference complementarity and experimental demonstration in a superconducting circuit

Quantum entanglement between an interfering particle and a detector for acquiring the which-path information plays central role enforcing Bohr's complementarity principle. However, quantitative relation this fringe visibility remains untouched upon initial mixed state. Here we find equality quantifying relation. Our characterizes how well interference pattern can be preserved when particle, initially carrying definite amount of coherence, is entangled, to certain degree, with detector. This provides connection in unified framework revealing entanglement-interference complementarity. We experimentally demonstrate superconducting circuit, where resonator serves as qubit. The measured qubit's Ramsey signal qubit-resonator exhibit complementary relation, agreement theoretical prediction.