Entanglement-interference complementarity and experimental demonstration in a superconducting circuit

TL;DR

This paper establishes a quantitative equality linking entanglement and interference visibility in a superconducting circuit, demonstrating how coherence is preserved or lost due to entanglement with a which-path detector.

Contribution

It introduces a new equality quantifying the entanglement-interference relation and experimentally verifies it using a superconducting circuit with a resonator as a which-path detector.

Findings

Measured fringe visibility and entanglement match the theoretical relation

Experimental results confirm the entanglement-interference complementarity

Demonstrates coherence preservation in a superconducting qubit system

Abstract

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