A delayed-choice quantum eraser experiment is an elaboration on the quantum eraser experiment that incorporates concepts considered in John Archibald Wheeler's delayed-choice experiment. The experiment was designed to investigate peculiar consequences of the well-known double-slit experiment in quantum mechanics, as well as the consequences of quantum entanglement.

Delayed-choice quantum eraser experiments are designed to investigate the following apparent paradox arising from the traditional double-slit experiment: if, upon observing a photon, one can deduce that it arrived at a detector by following a particular path, then "common sense" (which Wheeler and others challenge) says that it must have entered the double-slit device as a particle, whereas if the photon's path cannot be deduced, then it must have entered the double-slit device as a wave. By this logic, a spontaneous change in the mode of observation while the photon is in transit may force it to retroactively alter its initial "commitment" to exhibiting either wave-like or particle-like behavior. Wheeler pointed out that, if one imagines an experimental setup of interstellar proportions, this reasoning suggests that a last-minute decision made on Earth on how to observe a photon could alter a physical configuration established millions or even billions of years earlier.

While delayed-choice experiments might seem to allow decisions (about how to make measurements) to alter events that have already occurred by the time they have been made, this conclusion may only be reached by adopting a non-standard interpretation of quantum mechanics. Under the standard interpretation, a photon in transit is considered to be in a superposition of states only one of which is observed in the measurement.

In the basic double-slit experiment, a coherent beam of light (in practice, often a laser) is directed at two (parallel) narrow vertical slits in an otherwise solid barrier. If a detection screen is placed at a sufficient distance from the barrier on the other side, one will observe an interference pattern of alternating light and dark fringes. Other atomic-scale entities such as electrons are found to exhibit the same behavior when fired toward a double slit. By decreasing the brightness of the source sufficiently, individual particles that form the interference pattern are detectable. The emergence of an interference pattern suggests that each particle passing through the slits interferes with itself, and that therefore in some sense the particles are going through both slits at once. This is an idea that contradicts our everyday experience of discrete objects.

A well-known thought experiment, which played a vital role in the history of quantum mechanics (for example, see the discussion on Einstein's version of this experiment), demonstrated that if particle detectors are positioned at the slits, showing through which slit a photon goes, the interference pattern will disappear. This which-way experiment illustrates the complementarity principle that photons can behave as either particles or as waves, but cannot be simultaneously observed to be both a particle and a wave. Technical challenges of the thought experiment prevented realizations of this experiment before the 1970s; similar experiments can now be performed in undergraduate physics labs.

Which-path information and the visibility of interference fringes are complementary quantities, meaning that information about a photon's path can be observed, or interference fringes can be observed, but they cannot both be observed in the same trial. In the double-slit experiment, conventional wisdom held that observing the particles' path inevitably disturbed them enough to destroy the interference pattern as a result of the Heisenberg uncertainty principle.

In 1982, Scully and Drühl pointed out a workaround alternative to this interpretation. They proposed to save the information about which slit the photon went through - or, in their setup, from which atom the photon was re-emitted - in the excited state of that atom. At this point the which-path information is known and no interference is observed. However, one can "erase" this information by making the atom emit another photon and fall to the ground state. That on its own will not bring the interference pattern back, the which-path information can still be extracted from an appropriate measurement of the second photon. However, if the second photon is measured at a place where it could get to equally likely from any of the atoms, that successfully "erases" the which-path information. The original photon would now show the interference pattern (the position of its fringes depends on where exactly the second photon was observed, so that in the total statistics they average out and no fringes are seen). Since 1982, multiple experiments have demonstrated the validity of this so-called quantum "eraser". A form of the experiment closely matching Scully and Drühl concept was performed in 2000.

A simple version of the quantum eraser can be described as follows: Rather than splitting one photon or its probability wave between two slits, the photon is subjected to a beam splitter. If one thinks in terms of a stream of photons being randomly directed by such a beam splitter to go down two paths that are kept from interaction, it would seem that no photon can then interfere with any other or with itself.