Delayed-choice quantum erasers and the Einstein-Podolsky-Rosen paradox

Considering the delayed-choice quantum eraser using a Mach-Zehnder interferometer with a nonsymmetric beam splitter, we explicitly demonstrate that it shares exactly the same formal structure with the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment. Therefore, the effect of quantum erasure can be understood in terms of the standard EPR correlation. Nevertheless, the quantum eraser still raises a conceptual issue beyond the standard EPR paradox, if counterfactual reasoning is taken into account. Furthermore, the quantum eraser experiments can be classified into two major categories: the entanglement quantum eraser and the Scully-Dr\"uhl-type quantum eraser. These two types are formally equivalent to each other, but conceptually the latter presents a "mystery" more prominent than the former. In the Scully-Dr\"uhl-type quantum eraser, the statement that the which-way information can be influenced by the delayed-choice measurement is not purely a consequence of counterfactual reasoning but bears some factual significance. Accordingly, it makes good sense to say that the "record" of the which-way information is "erased" if the potentiality to yield a conclusive outcome that discriminates the record is eliminated by the delayed-choice measurement. We also reconsider the quantum eraser in the many-worlds interpretation (MWI), making clear the conceptual merits and demerits of the MWI.