A priori which-way information in quantum interference with unstable particles

If an unstable particle used in a two-path interference experiment decays before reaching a detector, which-way information becomes available that reduces the detected interference fringe visibility V. Here we argue that even when an unstable particle does not decay while in the interferometer, a priori which-way information is still available in the form of path predictability P which depends on the particle's decay rate Γ. We further demonstrate that in a matter-wave Mach-Zehnder interferometer using an excited atom with an appropriately tuned cavity, P is related to V through the duality relation P2+V2=1.