Entanglement-interference complementarity and experimental demonstration in a superconducting circuit

  1. Xin-Jie Huang,
  2. Pei-Rong Han,
  3. Wen Ning,
  4. Shou-Ban Yang,
  5. Xin Zhu,
  6. Jia-Hao Lü,
  7. Ri-Hua Zheng,
  8. Hekang Li,
  9. Zhen-Biao Yang,
  10. Qi-Cheng Wu,
  11. Kai Xu,
  12. Chui-Ping Yang,
  13. Dongning Zheng,
  14. Heng Fan,
  15. and Shi-Biao Zheng
Quantum entanglement between an interfering particle and a detector for acquiring the which-path information plays a central role for enforcing Bohr’s complementary principle, but the quantitative relation between this entanglement and the fringe visibility remains untouched upon. Here we find an equality for quantifying this relation. Our equality characterizes how well the interference pattern can be preserved when an interfering particle, initially carrying a definite amount of coherence, is entangled with a which-path detector to a certain degree. This equality provides a connection between entanglement and interference in the unified framework of coherence, revealing the quantitative entanglement-interference complementarity for the first time. We experimentally demonstrate this relation with a superconducting circuit, where a resonator serves as a which-path detector for an interfering qubit. The results demonstrate quantum entanglement is the mechanism for prohibiting any detector from acquiring which-path information without deteriorating the interference pattern, which was not confirmed previously.
arxiv pdf

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