Complementarity relations of a delayed-choice quantum eraser in a quantum circuit

Abstract

We propose a quantum circuit that emulates a delayed-choice quantum eraser via bipartite entanglement with the extension that the degree of entanglement is adjustable. This provides a broader setting to test complementarity relations between interference visibility and whichway distinguishability in the scenario that the which-way information is obtained through entanglement without direct contact with the quantum state for interference. The visibilitydistinguishability relations are investigated from three perspectives that differ in how the which-way information is taken into consideration. These complementarity relations can be understood in terms of entropic uncertainty relations in the information-theoretic framework and the triality relation that incorporates single-particle and bipartite properties. We then perform experiments on the quantum computers provided by the IBM Quantum platform to verify the theoretical predictions. We also apply the delay gate to delay the measurement of the which-way information to affirm that the measurement can be made truly in the "delayed-choice" manner.