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The Englert–Greenberger–Yasin duality relation, often called the Englert–Greenberger relation, relates the visibility, [math]\displaystyle{ V }[/math], of interference fringes with the definiteness, or distinguishability, [math]\displaystyle{ D }[/math], of the photons' paths in quantum optics. As an inequality: Although it is treated as a single relation, it actually involves two separate relations, which mathematically look very similar. The first relationship was first experimentally shown by Greenberger and Yasin in 1988. It was later theoretically derived by Jaeger, Shimony, and Vaidman in 1995. This relation involves correctly guessing which of the two paths the particle would have taken, based on the initial preparation. Here [math]\displaystyle{ D }[/math] can be called the predictability, and is sometimes denoted by [math]\displaystyle{ P }[/math]. A year later Englert, in 1996, apparently unaware of this result, derived a related relation which dealt with knowledge of the two paths using an apparatus. Here [math]\displaystyle{ D }[/math] is called the distinguishability. The significance of the relation is that it expresses quantitatively the complementarity of wave and particle viewpoints in double slit experiments. The complementarity principle in quantum mechanics, formulated by Niels Bohr, says that the wave and particle aspects of quantum objects cannot be observed at the same time. The Englert–Greenberger relation makes this more precise; an experiment can yield partial information about the wave and particle aspects of a photon simultaneously, but the more information a particular experiment gives about one, the less it will give about the other. The distinguishability [math]\displaystyle{ D }[/math] which expresses the degree of probability with which path of the particle is known, is a measure of the particle information, while the visibility of the fringes [math]\displaystyle{ V }[/math] is a measure of the wave information. The relation shows that they are inversely related, as one goes up, the other goes down.