Yes, the quantum erasure experiment has been conducted with interference, and it involves the storage of path information in qubits rather than classical bits. The experiment is known as the delayed-choice quantum eraser experiment.
In the traditional quantum eraser experiment, a photon is sent through a double-slit apparatus, which creates an interference pattern on a screen. The path of the photon can be determined by placing detectors near the slits, which destroys the interference pattern. However, in the delayed-choice quantum eraser experiment, the choice of whether to observe or erase the path information of the photon is made after the photon has already passed through the double-slit.
Here's a brief description of the experiment:
A photon is sent through a double-slit apparatus, creating an interference pattern on a screen.
The path information of the photon is recorded by detectors placed near the slits, which destroys the interference pattern.
The path information is then "erased" by adding an additional beam splitter and two detectors, which allow the interference pattern to re-emerge.
The key aspect of the experiment is that the choice to observe or erase the path information is made after the photon has passed through the double-slit, but before it reaches the final detectors.
The detection results at the final detectors are then correlated with the presence or absence of path information, demonstrating that the interference pattern can be either present or absent depending on whether the path information is known or erased.
In this experiment, the path information is typically encoded in qubits, which are quantum bits. Qubits can exist in superposition states, representing both 0 and 1 simultaneously. By manipulating the qubits, the path information can be stored and manipulated in a quantum manner, allowing for the observation or erasure of the path information to have an impact on the interference pattern.
The delayed-choice quantum eraser experiment highlights the counterintuitive nature of quantum mechanics, where the measurement or erasure of information can retroactively affect the behavior of particles. It demonstrates that the wave-particle duality and the interference pattern are deeply connected to the knowledge we have about the path information of particles, even if that knowledge is obtained after the particles have interacted with their environment.