Englert–Greenberger duality relation

The Englert–Greenberger–Yasin duality relation, often called the Englert–Greenberger relation, relates the visibility, ${\displaystyle V}$, of interference fringes with the definiteness, or distinguishability, ${\displaystyle D}$, 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 ${\displaystyle D}$ can be called the predictability, and is sometimes denoted by ${\displaystyle P}$. 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 ${\displaystyle D}$ is called the distinguishability.

...
Wikipedia