An Inequality Concerning Quantitative Duality in an Asymmetry Two-Way Interferometer

We reinvestigate the measures concerning the notion of duality of a quantum system (the ``quanton'') in an asymmetry two-way interferometer. A new measure of the which-way information is introduced, which is based on the fidelity F instead of the trace distance Q of the final states of the which-way detector. An improved inequality is derived to be V²≤(R₀²- P²)(1-F)², which is more stringent than the previous one of V²≤q(1-P²)(1-Q²).