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 which reduces the detected interference fringe visibility ${\cal V}$. Here we argue that even when an unstable particle does {\em not} decay while in the interferometer, {\em a priori} which-way information is still available in the form of path predictability ${\cal P}$ which depends on the particle's decay rate $\Gamma$. We further demonstrate that in a matter-wave Mach-Zehnder interferometer using an excited atom with an appropriately tuned cavity, ${\cal P}$ is related to ${\cal V}$ through the duality relation ${\cal P}^{2} + {\cal V}^{2} = 1$.