The Enigma of Delayed Choice Quantum Eraser

TL;DR

The paper analyzes delayed-choice quantum eraser experiments to clarify how Bohr's complementarity manifests when which-path information is available or erased, including delayed erasure after detection. It develops two formalisms, a two-path and a generalized n-channel eraser, and interprets results via an Einstein-Podolsky-Rosen–like entangled-state analogy to emphasize correlations over retrocausal changes. The key finding is that in the delayed mode the which-path information is always erased and interference can be recovered only by selecting an appropriate path-detector basis, with no signaling backward in time. This work resolves common interpretational confusions by showing that apparent retrocausality arises from correlational rather than causal mechanisms and provides a coherent framework for analyzing delayed-choice erasure experiments.

Abstract

The delayed-choice quantum eraser represents an interesting experiment that exemplifies Bohr's principle of complementarity in a beautiful way. According to the complementarity principle, in a two-path interference experiment, the knowledge of which path was taken by the particle and the appearance of interference are mutually exclusive. Even when the which-path information is merely retained in specific quantum path-markers, without being actually read, it suffices to eliminate interference. Nevertheless, if this path information is ``erased'' in some manner, the interference re-emerges, a phenomenon referred to as the quantum eraser. An intriguing aspect of this experiment is that if the path information is erased \emph{after} the particle has been detected on the screen, the interference still reappears, a phenomenon known as the delayed-choice quantum eraser. This observation has led to the interpretation that the particle can be influenced to exhibit characteristics of either a particle or a wave based on a decision made long after it has been registered on the screen. This idea has sparked considerable debate and discussions surrounding retrocausality. This controversy is reviewed here, and a detailed resolution provided.

Figures (6)

• Figure 1: Schematic diagram of a two-slit interference experiment. There are two possible paths a quanton can take, in arriving at the screen.
• Figure 2: A typical interference pattern in a two-slit interference in the presence of a which-way detector. The solid line represents the recovered interference corresponding to the path-detector state $|d_+\rangle$, the dashed line represents the recovered interference corresponding to the path-detector state $|d_-\rangle$. If one just detects all the quantons without bothering about the path detector, a washed out interference pattern (the dotted line) is obtained.
• Figure 3: Schematic diagram of a two-path, $n-$channel interference experiment. There are two possible paths a quanton can take, in arriving at the $n$ output detectors.
• Figure 4: A typical interference pattern for $n=10$ channels. All the quantons land only at odd numbered detectors, and none at even numbered ones. This represents a fringe pattern.
• Figure 5: Recovered interference patterns for $n=10$ channels, in the presence of a path detector. Corresponding to the path-detector state $|d_+\rangle$ all the quantons land only at odd numbered detectors. Corresponding to the path-detector state $|d_-\rangle$ all the quantons land only at even numbered detectors.